We provide probability practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on probability skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of probability Questions

Question No | Questions | Class |
---|---|---|

1 | Probability of an impossible event is | 12 |

2 | Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( boldsymbol{P}(overline{boldsymbol{A}} cap overline{boldsymbol{B}}) ) | 12 |

3 | In a binomial distribution mean is 4.8 and variance is ( 2.88, ) then the parameter ( n ) is A . 8 B. 12 c. 16 D. 20 | 12 |

4 | Once you toss a coin, you will get the result as head or tail. Doing this action is called an A . space B. sample c. experiment D. event | 12 |

5 | 7. The probability that A speaks truth is 5while the probability for The probability that they contradict 20041 each other when asked to speak on a fact is 111it distribution. | 12 |

6 | If ( S ) is a sample space ( P(A)=frac{1}{3} P(B) ) and ( S=A cup B ) where ( A ) and ( B ) are two mutually exclusive events, then ( boldsymbol{P}(boldsymbol{A})= ) A ( cdot frac{1}{4} ) в. ( frac{1}{2} ) ( c cdot frac{3}{4} ) D. | 12 |

7 | The probability of ( A= ) Probability of ( B= ) Probability of ( mathrm{C}=frac{1}{4} ) ( boldsymbol{P}(boldsymbol{A}) cap boldsymbol{P}(boldsymbol{B}) cap boldsymbol{P}(boldsymbol{C})=mathbf{0} . boldsymbol{P}(boldsymbol{B} cap boldsymbol{C})= ) 0 and ( P(A cap C)=frac{1}{8} . P(A cap B)=0 ) the probability that atleast one of the events ( A, B, C ) exists is? A ( cdot frac{5}{8} ) в. ( frac{37}{64} ) ( c cdot frac{3}{4} ) ( D ) | 12 |

8 | 18. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is (2004S) (a) 4/25 (b) 4/35 (c) 4/33 (d) 4/1155 | 11 |

9 | State and prove Addition theorem on probability. | 12 |

10 | B uch that P(AUB)=3/4, P( A A and B are events such that P(AUB)=3/4, P(A)=2/3 then PA B ) is (a) 5/12 (b) 3/8 (c) 5/8 (d) )=1/4, [2002] 1/4 A di dered | 11 |

11 | Which of the following cannot be the probability of an event? A ( cdot frac{2}{3} ) в. -1.5 c. ( 15 % ) D. 0.7 | 12 |

12 | ( A ) box ( B_{1} ) contains 1 white ball, 3 red balls and 2 black balls. Another box ( B_{2} ) contains 2 white balls, 3 red balls and 4 black balls. A third box ( B_{3} ) contains 3 white balls, 4 red balls and 5 black balls If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box ( B_{2} ) is A ( cdot frac{116}{181} ) в. ( frac{126}{181} ) c. ( frac{65}{181} ) D. ( frac{55}{181} ) | 12 |

13 | From a batch of 100 items of which 20 are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probabilities that the second item chosen is defective A ( cdot frac{2}{5} ) в. ( frac{19}{100} ) ( c cdot frac{1}{5} ) D. none of these | 12 |

14 | A card is drawn at random from a well shuffled card. find the probability of card drawn is a black king. A ( cdot frac{1}{26} ) B. ( frac{2}{26} ) c. ( frac{4}{26} ) D. None of the above | 12 |

15 | 8. One hundred identical coins, each with probability, p, of showing up heads are tossed once. If 0 < p < 1 and the probabilitity of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is (1988 – 2 Marks) (a) 1/2 (b) 49/101 (c) 50/101 (d) 51/101. 1 | 12 |

16 | The binomial distribution whose mean is 9 and the variance is 2.25 is ( ^{mathbf{A}} cdotleft(12, frac{1}{2}, frac{1}{2}right) ) B ( cdotleft(12, frac{2}{3}, frac{1}{3}right) ) ( ^{mathbf{c}} cdotleft(12, frac{5}{6}, frac{1}{6}right) ) D. ( left(12, frac{3}{4}, frac{1}{4}right) ) | 12 |

17 | A die has 6 faces marked by the given numbers as shown below: The die is thrown once. What is the probability of getting an integer greater than ( -mathbf{3} ? ) ( 1 3 longdiv { 2 3 } ) | 12 |

18 | How many outcomes are possible when a coin is tossed A. 2 times B. 3 times c. 4 times D. 5 times | 12 |

19 | A salesman has a ( 70 % ) chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers ( A ) and ( B ) enter, what is the probability that the salesman will sell the product to customer A or B? A . 0.98 B. 0.91 c. 0.70 D. 0.49 | 12 |

20 | In how many different ways can the letter of the word FINANCE be arranged? A . 5040 в. 2040 ( c .2520 ) D. 4080 E. None of these | 12 |

21 | In a test an examine either gusses or copies or knows the answer to a multiple choice question with ( m ) choices out of which exactly one is correct. The probability that he makes a guess is ( 1 / 3 ) and the probability that he copies the answer is 1/6. The probability that his answer is correct given that the copied it, is ( 1 / 8 . ) If the probability that he knew the answer to the question given that he correctly answered it is ( 120 / 141 ) find ( boldsymbol{m} ) | 12 |

22 | There are two coins, one unbiased with probability ( frac{1}{2} ) of getting heads and the other one is biased with probability ( frac{3}{4} ) of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiasedcoin was selected is A ( cdot frac{2}{3} ) в. ( frac{3}{5} ) c. ( frac{1}{2} ) D. ( frac{2}{5} ) | 12 |

23 | In a certain population ( 10 % ) of the people are rich, ( 5 % ) are famous and ( 3 % ) are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to A . 0.07 B. 0.08 c. 0.09 D. 0.12 | 12 |

24 | A die is thrown. Write the sample space. If ( A ) is the event that the number is a perfect square, write the event ( boldsymbol{A} ) using set notation. | 12 |

25 | For three events ( A, B ) and ( C, P( ) exactly one of the events ( A text { or } B text { occurs })=P( ) exactly one of the vents ( B ) or ( C ) occurs ( =P(text { exactly one of the events } C text { or } A ) occurs ( )=p ) and ( P( ) all the three events occur simultaneously ( )=p^{2}, ) where ( 0< ) ( boldsymbol{p}<frac{1}{2} ) Then the probability of atleast one of the three events ( A, B ) and ( C ) occurring is A ( cdot frac{3 p+2 p^{2}}{2} ) в. ( frac{p+3 p^{2}}{2} ) c. ( frac{3 p+p^{2}}{2} ) D. ( frac{3 p+2 p^{2}}{4} ) | 12 |

26 | Three numbers are chosen at random from the first 20 natural numbers. Then what is the probability that their product is odd? | 12 |

27 | If ( boldsymbol{P}(boldsymbol{A})=frac{1}{2}, boldsymbol{P}(boldsymbol{B})=0, ) then ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) ) is ( mathbf{A} cdot mathbf{0} ) B. c. Not defined D. | 12 |

28 | The probability that a two digit number selected at random will be a multiple of ‘3’ and not a multiple of ‘5’ is A ( cdot frac{2}{15} ) в. ( frac{4}{15} ) c. ( frac{1}{15} ) D. ( frac{4}{90} ) | 12 |

29 | Given two independent events ( A ) and ( B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} ) Find (i) ( P(A text { and not } B) ) (ii) P(neither A nor B) | 12 |

30 | If two numbers ( p ) and ( q ) are chosen randomly from the set {1,2,3,4} with replacement, then the probability that ( p^{2} leq 4 q ) is equal to A ( cdot frac{1}{4} ) B. ( frac{3}{16} ) ( c cdot frac{1}{2} ) D. ( frac{9}{16} ) E. ( frac{7}{16} ) | 12 |

31 | sleep. He classifies sleep activity in four stages: 1,2,3 and ( 4 . ) Stage 3 is the only stage considered to be deep sleep. Ajay goes to clinic for sleeping brainwashes analyzed. Doctor monitored the person’s brainwashes in ( 15- ) minute intervals, for 8 continuous hours, and categorized them into one of the four stages. The graph above shows this study. fone ( 15- ) minute time period is chosen at random, then the probability that the patient was in deep sleep during that time is ( frac{a}{b}, ) where ( a, b ) are co-primes. What is the value of ( a+b ? ) | 12 |

32 | A machine has three parts, ( A, B ) and ( C ) whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the probability that the machine will not stop working? A . 0.06 B. 0.16 c. 0.84 D. 0.94 | 12 |

33 | If ( A ) is required event and ( S ) is the sample space, ( boldsymbol{n}(boldsymbol{A})=mathbf{3}, boldsymbol{n}(boldsymbol{S})=mathbf{6} ) then find ( boldsymbol{P}(boldsymbol{A}) ) | 12 |

34 | The probability that an automobile will be stolen and found within one week is ( 0.0006 . ) The probability that an automobile will be stolen is ( 0.0015 . ) The probability that a stolen automobile will be found in one week is A . 0.3 B. 0.4 ( c .0 .5 ) D. 0.6 | 12 |

35 | Two symmetrical dice are thrown at a time. If the sum of points on them is 7 the chance that one of them will show a face with 2 points is A ( cdot frac{1}{8} ) в. ( frac{1}{3} ) ( c cdot frac{2}{3} ) D. | 12 |

36 | When a die is thrown, list the outcomes of an event of getting a prime number. A ( cdot{1,4,6} ) в. {2,3,5} D. None of these | 12 |

37 | If the probability distribution of a random variable x is ( boldsymbol{X}=boldsymbol{x}_{1}: quad-2 quad-1 quad mathbf{0} quad mathbf{1} quad mathbf{2} quad mathbf{3} ) ( boldsymbol{p}left(boldsymbol{X}=boldsymbol{x}_{1}right): mathbf{0 . 1} quad boldsymbol{k} quad mathbf{0 . 2} quad mathbf{2 k} mathbf{0 . 3} boldsymbol{k} ) then the mean of ( x ) is A . 0.6 B. 0.8 ( c .1 .0 ) D. 0.3 | 12 |

38 | Determine the binomial distribution whose mean is 4 and variance 3 | 12 |

39 | In a hand at whist find the chance that a specified player holds both the king and queen of trumps. Note:Whist is a game of cards in which a standard pack of 52 cards is used.The game is played in pairs.In each round, a suit is randomly selected as ‘Trump’ which gets a preference over other suits for that particular round. | 12 |

40 | Three coins are tossed. Describe two events ( A ) and ( B ) which are mutually exclusive. | 12 |

41 | A card is down & replaced in ordinary pack of 52 playing cards. Minimum number of times must a card be drawn so that there is atleast an even chance of drawing a heart, is A . 2 B. 3 ( c cdot 4 ) D. more than four | 12 |

42 | Consider two events ( A, B ) of an zperiment satisfying ( boldsymbol{P}(boldsymbol{A} cup overline{boldsymbol{B}})=frac{mathbf{3}}{boldsymbol{4}} boldsymbol{&} ) ( P(B)=frac{1}{2}, ) then ( Pleft(frac{A}{B}right) ) is equal to A ( cdot frac{1}{3} ) B. ( frac{1}{4} ) ( c cdot frac{1}{2} ) D. | 12 |

43 | A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is A ( cdot frac{5}{24} ) в. ( frac{13}{24} ) ( c cdot frac{1}{4} ) D. ( frac{2}{3} ) | 12 |

44 | Two coins are tossed. Find the probability, if ( boldsymbol{P} ) is the event of getting two head | 12 |

45 | A coin is tossed and a single 6 -sided die is rolled. Find the probability of landing on the tail side of the coin and rolling 4 on the die. A ( cdot frac{1}{12} ) в. ( frac{6}{5} ) ( c cdot frac{4}{3} ) D. ( frac{3}{4} ) | 12 |

46 | ( A ) and ( B ) are events with ( P(A)=0.5, P(B)= ) 0.4 and ( P(A cap B)=0.3 . ) Find the probability that: (i) A does not occur (ii) Neither ( A ) and nor ( B ) occurs | 12 |

47 | A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black? A ( cdot frac{31}{153} ) в. ( frac{30}{153} ) c. ( frac{33}{153} ) D. ( frac{32}{153} ) | 12 |

48 | Let ( A ) and ( B ) be two events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) . ) Then Statement ( 1: P(A cap bar{B})=P(bar{A} cap B)= ) 0 Statement 2: If ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})=mathbf{1} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 12 |

49 | Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head? A ( cdot frac{1}{4} ) в. ( frac{2}{3} ) ( c cdot frac{1}{3} ) D. ( frac{3}{4} ) | 12 |

50 | A factory produces bulbs. The probability that one bulb is defective is ( frac{1}{50} ) and they are packed in boxes of ( 10 . ) If the probability that none of the bulbs is defective from a single box is ( left(frac{49}{50}right)^{k} ) then value of ( k ) is | 12 |

51 | Let ( X ) and ( Y ) be two random variables. The relationship ( boldsymbol{E}(boldsymbol{X} boldsymbol{Y})=boldsymbol{E}(boldsymbol{x}) cdot(boldsymbol{Y}) ) holds. A. Always B. If ( E(X+Y)=E(X)+E(Y) ) is true c. If ( X ) and ( Y ) are independent D. If ( X ) can be obtained from ( Y ) by a linear transformation | 12 |

52 | ( A ) and ( B ) each throw a die. The probability that ( A^{prime} ) ‘s throw is not greater than B’s is A ( cdot frac{21}{36} ) в. ( frac{12}{35} ) c. ( frac{7}{12} ) D. ( frac{5}{12} ) | 12 |

53 | If a random variable ( X ) follows binomial distribution with mean 3 and variance ( frac{3}{2}, ) and ( P(X leq 5)=frac{63}{2^{x}}, ) then the value of ( ^{prime} x^{prime} ) is | 12 |

54 | Suppose ( boldsymbol{E}_{1}, boldsymbol{E}_{2}, boldsymbol{E}_{3} ) be three mutually exclusive events such that ( boldsymbol{P}left(boldsymbol{E}_{i}right)=boldsymbol{p}_{i} ) for ( boldsymbol{i}=mathbf{1}, mathbf{2}, mathbf{3} ) ( operatorname{then} Pleft(E_{1} cap E_{2}^{prime}right)+Pleft(E_{2} cap E_{3}^{prime}right)+ ) ( boldsymbol{P}left(boldsymbol{E}_{3} cap boldsymbol{E}_{1}^{prime}right) ) equals A ( cdot p_{1}left(1-p_{2}right)+p_{2}left(1-p_{3}right)+p_{3}left(1-p_{1}right) ) В. ( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} ) c. ( p_{1}+p_{2}+p_{3} ) D. None of these | 12 |

55 | Three integers are chosen at random without replacement from the 1st 20 integers. The probability that their product is even is A ( cdot frac{16}{19} ) в. ( frac{17}{19} ) c. ( frac{18}{19} ) D. ( frac{15}{19} ) | 12 |

56 | If ( C ) and ( D ) are two events such that ( mathbf{C} subset mathbf{D} ) and ( mathbf{P}(mathbf{D}) neq mathbf{0}, ) then the correct statement among the following is ( ^{mathbf{A}} cdot pleft(frac{C}{D}right)=mathrm{P}(mathrm{C}) ) ( ^{mathbf{B}} cdot pleft(frac{C}{D}right) geq mathrm{P}(mathrm{C}) ) ( ^{c} cdot pleft(frac{C}{D}right)<mathrm{P}(mathrm{C}) ) ( Pleft(frac{C}{D}right)=frac{P(D)}{P(C)} ) | 12 |

57 | Out of 800 families with 4 children each, the expected number of families having atleast one boy is A . 550 B. 50 c. 750 D. 300 | 12 |

58 | A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a face card. ( A cdot frac{8}{13} ) в. ( frac{3}{13} ) c. ( frac{4}{13} ) D. ( frac{1}{4} ) | 12 |

59 | Probability of any event ( boldsymbol{x} ) lies A. ( 0<x<1 ) в. ( 0 leq x<1 ) c. ( 0 leq x leq 1 ) D. ( 1<x<2 ) | 12 |

60 | There are three coins. One is a two- headed coin (having head on both faces), another is a biased coin that comes up heads ( 75 % ) of the times and third is also a biased coin that comes up tails ( 40 % ) of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed ( operatorname{coin} ? ) | 12 |

61 | In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is: (i) the name of a girl (ii) the name of a boy | 12 |

62 | For the events ( boldsymbol{A} ) and ( boldsymbol{B}, boldsymbol{P}(boldsymbol{A})= ) ( frac{3}{4}, P(B)=frac{1}{5}, P(A cap B)=frac{1}{20} ) then ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})= ) ( A cdot frac{1}{4} ) B. ( frac{1}{15} ) ( c cdot frac{3}{4} ) D. | 12 |

63 | Red on first draw and white on second draw | 12 |

64 | A number ( x ) is selected at random from the numbers 1,4,9,16 and another number ( y ) is selected at random from the number ( 1,2,3,4 . ) Find the probability that the value of ( x y ) is more than 16 | 12 |

65 | A student appears for tests, I, II and III The student is successful if he passes in tests I, Il or I, Ill. The probabilities of the student passing in tests I, II and III are espectively ( mathrm{p}, mathrm{q} ) and ( frac{1}{2} . ) If the probability of the student to be successful is ( frac{1}{2} ) then A ( cdot p(1+q)=1 ) B. ( q(1+p)=1 ) c. ( p q=1 ) D. ( frac{1}{p}+frac{1}{q}=1 ) | 12 |

66 | ( A, B, C ) are three events for which ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{C})= ) ( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 2 .} ) If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup ) ( C) geq 0.85 ) then the interval of values of ( boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is В. [0.55,0.7] D. none of these | 12 |

67 | In an examination, the probability of a candidate solving a question is ( frac{1}{2} . ) Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions? A ( cdot frac{1}{64} ) в. ( frac{3}{16} ) ( c cdot frac{1}{2} ) D. ( frac{13}{16} ) | 12 |

68 | If ( P(A)=P(B), ) then ( A cdot A ) and ( B ) are the same events B. ( A ) and ( B ) must be same events C. ( A ) and ( B ) may be different events D. A and B are mutually exclusive events. | 12 |

69 | A boy has a collection of blue and green marbles. The number of blue marbles belong to the sets ( 2,3,4,13 . ) If two marbles are chosen simultaneously and at random from his collection, then the probability that they have different colour is ( 1 / 2 . ) Possible number of blue marbles is: A . 2 B. 3 ( c cdot 6 ) D. 10 | 12 |

70 | n different toys are to be distributed among n children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy | 12 |

71 | A letter is known to have come either from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or ( boldsymbol{C A L} boldsymbol{C U T T A} ) On the envelope just two consecutive letters ( T A ) are visible. What is the probability that the letter came from CALCUTTA? ( A cdot frac{4}{11} ) B. ( frac{7}{11} ) ( c cdot frac{2}{11} ) D. None of these | 12 |

72 | A die is thrown once. If ( A ) is the event “the number appearing is a multiple of ( 3 ” ) and ( B ) is the event “the number appearing is even” Are the event A and B independent? | 12 |

73 | Let ( X ) denote the number of time tail appear in ( n ) tosses of a fair coin. If ( boldsymbol{P}(boldsymbol{X}=mathbf{1}), boldsymbol{P}(boldsymbol{X}=mathbf{2}) ) and ( boldsymbol{P}(boldsymbol{X}=mathbf{3}) ) are in A.P., then value of ( boldsymbol{n} ) is ( mathbf{A} cdot mathbf{9} ) B . 2 ( c cdot 7 ) D. None of these | 12 |

74 | The probability of selecting a rotten apple randomly from a heap of 900 apples is ( 0.18 . ) What is the number of rotten apples in the heap? | 12 |

75 | Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3 2} ) | 12 |

76 | In an entrance test is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7 . The probability of passing at least of them is ( 0.95 . ) What is the probability of passing both? | 12 |

77 | Twelve players ( S_{1}, S_{2}, dots, S_{12} ) play in a chess tournament. They are divided into six pairs at random. From each pair a winner is decided. It is assumed that all players are of equal strength. The probability that exactly one of ( S_{1} ) and ( S_{2} ) is among the six winners is A ( cdot frac{6}{11} ) в. ( frac{5}{11} ) c. ( frac{4}{11} ) D. None of these | 12 |

78 | The variance of the random variable ( x ) whose probability distribution is given by ( boldsymbol{X}=boldsymbol{x}_{i}: quad-1 quad, boldsymbol{0}, quad+1 ) ( boldsymbol{p}left(boldsymbol{X}=boldsymbol{x}_{i}right): mathbf{0 . 4}, mathbf{0 . 2}, quad mathbf{0 . 4} ) is A . 0.4 B. 0.6 ( c .0 .8 ) D. 1.0 | 12 |

79 | Let ( A ) be a set containing ( n ) elements. ( A ) subset ( P ) of the set ( A ) is chosen at random.The set A is reconstructed by replacing the elements of ( P ) and another subset ( Q ) of ( A ) is chosen at random. The probability that ( boldsymbol{P} cap boldsymbol{Q} ) contains exactly ( m(m<n) ) elements is ( ^{A} cdot frac{3^{n cdot m} cdot m^{n}}{^{n}} ) В. ( frac{n_{C_{m}} times 3^{m}}{4^{n}} ) c. ( frac{n_{m_{m} times 3^{n . m}}}{4^{n}} ) D. None of these | 12 |

80 | The chances of defective screws in three boxes ( A, B ) and ( C ) are ( frac{1}{5}, frac{1}{6}, frac{1}{7} ) respectively. A box is selected at random and a screw drawn from it at random, is found to be defective. The probability that it came from the | 12 |

81 | A card is draw from a well-shuffled pack of 52 cards. What is the probability that a card will be a king? | 12 |

82 | Suppose a girl throws a die. If she gets 1 or ( 2, ) she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or ( 6, ) she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one tail’, what is the probability that she threw 3,4,5 or 6 with the die? | 12 |

83 | The probability that Dhoni will hit century in every ODI matches he plays is ( frac{1}{5} ). If he plays 6 matches in World Cup ( 2011, ) the probability that he will score 2 centuries is: A ( cdot frac{768}{3125} ) в. ( frac{2357}{3125} ) c. ( frac{2178}{3125} ) D. ( frac{412}{3125} ) | 12 |

84 | A coin is tossed 5 times. The probability of 2 heads and 3 tails is: A ( cdot frac{11}{16} ) B. ( frac{5}{16} ) c. ( frac{11}{32} ) D. ( frac{5}{32} ) | 12 |

85 | A box contains 20 identical balls of which 5 are white and 15 black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn fro the ( 3^{r d} ) time on ( 6^{t h} ) drawn is | 12 |

86 | If ( A ) is any event in a sample space, then ( boldsymbol{P}(overline{boldsymbol{A}})=mathbf{1}+boldsymbol{P}(boldsymbol{A}) ) A. True B. False c. Either D. Neither | 12 |

87 | Fifteen coupons are numbered ( 1,2, ldots . .15 ) respectively. Three coupons are selected at random without replacement. The probability that the maximum number on the selected coupon is ( 9, ) is A ( cdot 4 / 65 ) в. ( 3 / 65 ) ( mathrm{c} cdot 1 / 13 ) D. None of these | 12 |

88 | A box contain card number 11 to ( 123 . ) A card is drawn at random from the find the probability that the number on the drawn card is (ii) a multiple of 7 | 12 |

89 | For any two events ( A ) and ( B ) in a sample space This question has multiple correct options ( ^{mathbf{A}} cdot p(A / B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true B ( cdot P(A cap B)=P(A)-P(bar{A} cap bar{B}) ) does not hold. ( mathbf{c} cdot P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( A ) and ( B ) are independent D ( cdot P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint. | 12 |

90 | From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honours of the same suit. | 12 |

91 | State which of the following variables are continuous and which are discrete: a)number of children in your class b) distance traveled by a car c) sizes of shoes d) time e) number of patients in a hospital | 12 |

92 | Which of the following experiments have equally likely outcomes? (a) A driver attempts to start a car. The car starts or does not start. (b) A player attempts to shoot a basketball. She/he shoots or misses the shot. (c) A trial is made to answer a true-false question. The answer is right or wrong. (d) A baby is born. It is a boy or a girl. | 12 |

93 | If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) then find ( boldsymbol{P}(boldsymbol{A} cap overline{boldsymbol{B}}) ) | 12 |

94 | If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{B})=frac{1}{5} ) then This question has multiple correct options A ( cdot P(A cup B)=frac{3}{5} ) в. ( P(A / B)=frac{1}{2} ) c. ( P(A / A cup B)=frac{5}{6} ) D cdot ( Pleft(A cap B / A^{prime} cup B^{prime}right)=0 ) | 12 |

95 | A random variable ( boldsymbol{X} ) has the following probability distribution: Determine (i) ( k ) (ii) ( boldsymbol{P}(boldsymbol{X}boldsymbol{6}) ) (iv) ( boldsymbol{P}(mathbf{0}<boldsymbol{X}<mathbf{3}) ) begin{tabular}{|c|c|c|c|c|c|c|c|c|} hline ( mathrm{X} ) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \ hline ( mathrm{P}(mathrm{X}) ) & 0 & ( k ) & ( 2 k ) & ( 2 k ) & ( 3 k ) & ( k^{2} ) & ( 2 k^{2} ) & ( 7 k^{2}+k ) \ hline end{tabular} | 12 |

96 | If ( boldsymbol{E} ) and ( boldsymbol{F} ) are events such that ( boldsymbol{P}(boldsymbol{E})= ) ( frac{1}{4}, P(F)=frac{1}{2} ) and ( P(E a n d F)=frac{1}{8} ) find (i) ( P(E text { or } F) ) (ii) ( P(text { not } E text { and } operatorname{not} F) ) | 12 |

97 | Three numbers are chosen at random without replacement from ( 1,2, ldots .10 . ) The probability that the minimum of the chosen numbers is 3 , or their maximum is ( 7, ) is A ( cdot frac{7}{40} ) B. ( frac{5}{40} ) c. ( frac{11}{40} ) D. None of these | 12 |

98 | A box contains 100 tickets numbered ( 1,2, dots .100 . ) Two tickets are chosen at random. It is given that the minimum number on the two chosen tickets is not more than ( 10 . ) The maximum number on them is 5 with probability. A. в. c. ( frac{1}{90} ) D. | 12 |

99 | In a test an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he make, a guess is ( frac{1}{3} ) and the probability that he copies the answer is ( frac{1}{6} . ) The probability that his answer is correct given that he copied it is ( frac{1}{8} . ) Find the probability that he knew the answer to the question, given that he correctly answered it. | 12 |

100 | If two events ( A ) and ( B ) are such that ( boldsymbol{P}(boldsymbol{A})=cdot boldsymbol{2}, boldsymbol{P}(boldsymbol{B})=cdot boldsymbol{3} ) and ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) ( cdot 4 ) then ( P(A cap B) ) equals? A . 0.2 B. 0.1 ( c cdot 0.3 ) D. None of these | 12 |

101 | What are the possible number of outcomes if a card is drawn from a pack of 52 cards? A . 20 B . 30 ( c cdot 42 ) D. 52 | 12 |

102 | Find the probability distribution of the number of doublets in three throws of a pair of dice | 12 |

103 | A bag contain 4 white and 2 black balls. Two balls are drawn at random. The probability that they are of the same colour is A ( cdot frac{5}{7} ) B. c. ( frac{7}{15} ) D. ( frac{1}{15} ) | 12 |

104 | If ( A ) and ( B ) are two events such that ( mathbf{2} boldsymbol{P}(boldsymbol{A})=mathbf{3} boldsymbol{P}(boldsymbol{B}), ) where ( mathbf{0}<boldsymbol{P}(boldsymbol{A})< ) ( P(B)<1, ) then which one of the following is correct? A. ( P(A mid B)<P(B mid A)<P(A cap B) ) в. ( P(A cap B)<P(B mid A)<P(A mid B) ) c. ( P(B mid A)<P(A mid B)<P(A cap B) ) ( D(A cap B)<P(A mid B)<P(B mid A) ) | 12 |

105 | Two dice are thrown. The number of sample points in the sample space when six does not appear on any one side is A . 11 B . 30 c. 18 D. 25 | 12 |

106 | In 50 tosses of coin tail appears 32 times. If a coin is tossed random, what is the probability of getting head? | 12 |

107 | 20 card are numbered from 1 to ( 20 . ) One card is drawn at random. What is the probability that the number on the card is greater than ( 12 ? ) A ( cdot frac{2}{3} ) B. ( frac{1}{2} ) ( c cdot frac{2}{5} ) D. None of these | 12 |

108 | 11. The probability of drawing an ace from a deck of cards is 15 (a) à (d) 52 T .. . hat in the chance that tomorrow will be | 11 |

109 | Find the variance of numbers obtained on thrown an unbiased die. | 12 |

110 | A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is A ( cdot frac{3}{8} ) в. ( frac{1}{8} ) ( c cdot frac{1}{4} ) D. | 12 |

111 | ( X ) has three children in his family. The probability of one girl and two boys is…… A ( cdot frac{1}{8} ) B. ( frac{1}{2} ) ( c cdot frac{1}{4} ) D. ( frac{3}{8} ) | 12 |

112 | A computer producing factory has only two plants ( T_{1} ) and ( T_{2} ). Plant ( T_{1} ) produces ( 20 % ) and plant ( T_{2} ) produces ( 80 % ) of total computers produced. ( 7 % ) of computers produced in the factory turn out to be defective. It is known that ( P ) (computer turns out to be defective given that it is produced in plant ( T_{1} ) ) ( =10 P ) (computer turns out to be defective given that it is produced in plant ( T_{2} ) ). where ( P(E) ) denotes the probability of an event ( E . ) A computer produced in the factory is randomly selected and it does not turn out ot be defective. Then the probability that it is produced in plant ( T_{2} ) is A ( cdot frac{36}{73} ) в. ( frac{47}{79} ) c. ( frac{78}{93} ) D. ( frac{75}{83} ) | 12 |

113 | From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at random. Let the random variable X denote the number of defective items in the sample. If the sample is drawn without replacement, find the probability distribution of ( X ) | 12 |

114 | If ( frac{1+4 p}{4}, frac{1-p}{2}, frac{1-2 p}{2} ) are probabilities of three mutually exclusive events, then A ( cdot frac{1}{3} leq p leq frac{1}{2} ) в. ( frac{1}{3} leq p leq frac{2}{3} ) c. ( frac{1}{6} leq p leq frac{1}{2} ) D. None of these | 12 |

115 | two players ( A ) and ( B ) play a series of games of chess. The winning players in any games gets 1 points while the losing plays get 0 points. The player who achievers 4 point first, wins the series. If no game ends in draw, find the Number of ways in which the series is can be won by ( A ) | 12 |

116 | ( A ) is a set containing ( n ) elements. Two subsets ( P ) and ( Q ) of ( A ) are chosen at random. (P and Q may have elements in common). The probability that ( boldsymbol{P} cup boldsymbol{Q} neq ) ( A ) is A ( cdot(3 / 4)^{n} ) B. 1/4n c. ( ^{n} C_{2} / 2^{n} ) D. ( 1-(3 / 4)^{n} ) | 12 |

117 | ( A ) and ( B ) are two events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{mathbf{3}}{mathbf{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= ) ( frac{1}{4}, P(bar{A})=frac{2}{3} ; operatorname{then} P(bar{A} cap B) ) is A ( .1 / 12 ) в. ( 5 / 12 ) c. ( 4 / 9 ) D. ( 1 / 3 ) | 12 |

118 | If for two events ( A ) and ( B, P(A cup B)= ) ( frac{1}{2}, P(A cap B)=frac{2}{5} ) and ( operatorname{then} Pleft(A^{c}right)+ ) ( boldsymbol{P}left(boldsymbol{B}^{c}right) ) equals A ( cdot frac{4}{5} ) в. c. ( frac{11}{10} ) D. None of these | 12 |

119 | An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is A ( cdot frac{1}{4} ) B. ( frac{2}{3} ) c. ( frac{1}{5} ) ( D ) | 12 |

120 | A fair coin is tossed 99 times. If ( X ) is the number of times heads occur then ( P(X= ) r) is maximum when ( r ) is ( mathbf{A} cdot 49 ) B. 50 c. 51 D. none of these | 12 |

121 | If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{1} / 2 ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{5} ) then This question has multiple correct options A ( cdot P(A cup B)=frac{3}{5} ) B. ( P(A mid B)=frac{1}{2} ) ( ^{mathbf{c}} cdot P(A mid A cup B)=frac{5}{6} ) D . ( Pleft[(A cup B) midleft(A^{prime} cup B^{prime}right)right]=0 ) | 12 |

122 | ff ( P(E)=0.05, ) what is the probability of not ( ^{prime} boldsymbol{E}^{prime} ) ? | 12 |

123 | A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least 3 bowlers is ( A cdot frac{7}{13} ) B. ( frac{11}{15} ) c. ( frac{12}{13} ) D. None of these. | 12 |

124 | If three events ( A, B, C ) are mutually exclusive, then which one of the following is correct? A ( cdot P(A cup B cup C)=0 ) B . ( P(A cup B cup C)=1 ) c. ( P(A cap B cap C)=0 ) D cdot ( P(A cap B cap C)=1 ) | 12 |

125 | Only one subject A . 0.72 B. 0.36 c. 0.48 D. 0.24 | 12 |

126 | If ( A ) and ( B ) are two events, then, ( 1+ ) ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})-boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(boldsymbol{A}) ) is equal to ( mathbf{A} cdot P(bar{A} cup bar{B}) ) B ( cdot P(A cap bar{B}) ) ( mathbf{c} cdot P(bar{A} cap B) ) D ( cdot P(A cup B) ) E ( cdot P(bar{A} cap bar{B}) ) | 12 |

127 | The number of ways of arraigning 6 players to throw the cricket ball so that the oldest player may not throw first is A .120 в. 600 ( c .720 ) D. 715 | 12 |

128 | The probability of an event ( A+ ) Probability of the event ‘not ( A^{prime}= ) | 12 |

129 | There are 30 tickets numbered from 1 to 30 in a box. A ticket is drawn at random. If ( A ) is the event that the number on the ticket is a prime number less than 15 write the sample space ( S, n(S) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) ) | 12 |

130 | The probability that the value of certain stock will remain the same is ( 0.46 . ) The probability that its value will increase by Rs. 0.50 or Re. 1 per share are respectively 0.17 and 0.23 and the probability that its value will decrease by Rs. 0.25 per share is 0.14 . The expected gain per share is A . Rs. 0.75 B. Rs. 0.25 c. Rs. 0.28 D. Rs. 0.50 | 12 |

131 | Consider the following relations ( (1) boldsymbol{A}-boldsymbol{B}=boldsymbol{A}-(boldsymbol{A} cap boldsymbol{B}) ) (2) ( boldsymbol{A}=boldsymbol{A}-(boldsymbol{A} cap boldsymbol{B}) cup(boldsymbol{A}-boldsymbol{B}) ) (3) ( boldsymbol{A}-(boldsymbol{A} cup boldsymbol{C})=(boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{A}-boldsymbol{C}) ) Which of these is correct A . 1 and 3 B. 2 only ( c cdot 2 ) and 3 D. 1 and 2 | 12 |

132 | If ( P(A)=frac{1}{3}, P(B)=frac{1}{2} ) and ( A, B ) are mutually exclusive, find ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right) ) A ( cdot frac{5}{6} ) B. ( c cdot frac{1}{5} ) D. | 12 |

133 | While doing any experiment, there will be a possible outcome which is called A. An impossible event B. A sure event c. An exhaustive event D. A complementary event | 12 |

134 | An old man while dialing a 7 digit telephone number remembers that the first four digits consists of one ( 1^{prime} s, ) one ( 2^{prime} s ) and two ( 3^{prime} s . ) He also remembers that the fifth digit is either a 4 or 5 while has no memorizing of the sixth digit, he remembers that the seventh digit is 9 minus the sixth digit. Maximum number if distinct trails he has to try make sure that he dials the correct telephone number, is A . 360 B . 240 c. 216 D. none | 12 |

135 | For the following distribution function ( F(x) ) of a r.v ( X ) is given [ begin{array}{ccccc} x & 1 & 2 & 3 & 4 \ F(x) & 0.2 & 0.37 & 0.48 & 0.62 end{array} ] Then ( P(3<x leq 5)= ) A . 0.48 в. 0.37 c. 0.27 D. 1.47 | 12 |

136 | A die is thrown. If ( A ) is the event that the number on upper face is a prime, then write sample space and event ( boldsymbol{A} ) in set notation. | 12 |

137 | ( ln ) a shop ( X, 30 ) tin pure ghee and 40 tin adultered ghee are kept for sale while in shop ( Y, 50 ) tin pure ghee and 60 tin adultered ghee are there. One tin of ghee is purchased from one of the shops randomly and it is found to be adultered. Find the probability that it is purchased from shop B. | 12 |

138 | In a meeting, ( 70 % ) of the members favour and ( 30 % ) oppose a certain proposal. A member is selected at random and we take ( boldsymbol{X}=mathbf{0} ) if he opposed, and ( X=1 ) if he is in favour. Find ( boldsymbol{E}(boldsymbol{X}) ) and ( boldsymbol{V} boldsymbol{a} boldsymbol{r}(boldsymbol{X}) ) | 12 |

139 | 14. For the three events A, B, and C, P (exactly one of the events A or B occurs) = P (exactly one of the two events B or C occurs) = P(exactly one of the events C or A occurs) =p and P (all the three events occur simultaneously) = p-, where 0<p<1/2. Then the probability of at least one of the three events A, B and C occurring is (1996 – 2 Marks) (a) 3p+2p2 (b) P+3p? | (@) P+3p? (d) 3p+2p? | 11 |

140 | The mean and standard deviation of a random variable ( X ) are 10 and 5 respectively. Find. ( boldsymbol{E}left(left(frac{boldsymbol{x}-mathbf{1 0}}{mathbf{5}}right)^{2}right) ) | 12 |

141 | A manufacturer has three machine operators ( A, B ) and ( C . ) The first operator ( A ) produces ( 1 % ) defective items, whereas the other two operators ( B ) and ( C ) produce ( 5 % ) and ( 7 % ) defective items respectively. ( A ) is on the job for ( 50 % ) of the time, ( B ) is on the job for ( 30 % ) of the time and ( C ) is on the job for ( 20 % ) of the time. A defective item is produced, what is the probability that it was produced by ( boldsymbol{A} ) ? | 12 |

142 | There are two small boxes ( A ) and ( B ). ( ln A ) there are 9 white beads and 8 black beads. ( ln B ) there are 7 white and 8 black beads. We want to take a bead from a box. (a) What is the probability of getting a white bead from each box? (b) ( A ) white bead and a black bead are added to box ( B ) an then a bead is taken from it. What is probability of getting a white bead from it. | 12 |

143 | If ( bar{E} ) and ( bar{F} ) are complementary events of E and F respectively and if ( 0< ) ( boldsymbol{P}(boldsymbol{F})<1, ) then This question has multiple correct options A ( cdot P(E / F)+P(bar{E} / F)=1 ) B . ( P(E / F)+P(E bar{F})=1 ) c. ( P(bar{E} / F)+P(E bar{F})=1 ) D . ( P(E bar{F})+P(bar{E} bar{F})=1 ) | 12 |

144 | Let the p.m.f. of a random variable ( boldsymbol{X} ) be ( P(x)=frac{3-x}{10} ) for ( x=-1,0,1,2 ) otherwise Then ( boldsymbol{E}(boldsymbol{X}) ) is ( mathbf{A} cdot mathbf{1} ) B . 2 c. 0 D. – | 12 |

145 | A fair coin is tossed ( n ) times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then value of ( n ) is A .24 B. 48 c. 14 D. 16 | 12 |

146 | If a letter is selected at random from the letters of the word LOGARITHMS, then what is the probability that it will be a consonant? | 12 |

147 | When a die is thrown, list the outcomes of an event of getting: A number greater than 5 ( mathbf{A} cdot mathbf{5} ) B. 4 ( c .6 ) D. 3 | 12 |

148 | A man takes a step forward with probability 0.4 and backward with probability 0.6. Suppose the man takes 11 steps and ( p_{r} ) denotes the probability that the man is ( r ) steps away from his initial position, then value of | 12 |

149 | The probability of sample space is A . B. ( c cdot 1 ) D. None of these | 12 |

150 | A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability that the lot contains exactly 3 defective articles is ( 0.6 . ) Article are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelfth testing? | 12 |

151 | The expectation of the number of heads in 15 tosses of a coin is ( frac{x}{2} . ) The value of ( x ) is | 12 |

152 | Box-I contains 5 red and 4 white balls while box-ll contains 4 red and 2 white balls. A fair die is thrown. If it turns up a multiple of ( 3, ) a ball is drawn, from boxelse a ball is drawn from box-II. The probability that the ball drawn is white is ( frac{a}{27} . ) Find ( a ) | 12 |

153 | Suppose a girl throws a die. If she gets a 5 or ( 6, ) she tosses a coin three times and notes the number of heads. If she gets 1,2,3 or ( 4, ) she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,3 or 4 with the die? | 12 |

154 | If ( bar{E} ) and ( bar{F} ) are the complementary events of events ( boldsymbol{E} ) and ( boldsymbol{F} ) respectively and if ( mathbf{0}<boldsymbol{P}(boldsymbol{F})<mathbf{1}, ) then ( ^{mathbf{A}} cdot_{P}left(frac{E}{F}right)+Pleft(frac{bar{E}}{F}right)=1 ) в. ( quad Pleft(frac{E}{F}right)+Pleft(frac{E}{bar{F}}right)=1 ) ( ^{mathbf{c}} cdot_{P}left(frac{bar{E}}{F}right)+Pleft(frac{E}{bar{F}}right)=1 ) ( Pleft(frac{E}{bar{F}}right)+Pleft(frac{bar{E}}{bar{F}}right)=1 ) | 12 |

155 | If ( A ) and ( B ) are two events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 7} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 2} ) then ( boldsymbol{P}(boldsymbol{B}) ) is equal to A . 0.1 B. 0.3 ( c .0 .5 ) ( D ) | 12 |

156 | Let ( A, B, C ) be three events such that ( A ) and ( mathrm{B} ) are independent and ( boldsymbol{P}(boldsymbol{C})=mathbf{0} ) then events ( A, B, C ) are A. independent B. pairwise independent but not totally independent C. ( P(A)=P(B)=P(C) ) D. none of these | 12 |

157 | If a coin is tossed 3 times, then the number of outcomes will be? | 12 |

158 | A class has 15 students whose ages are 14,17,15,14,21,17,19,20,16,18,20,17,16 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age ( X ) of the selected student is recorded. What is the probability distribution of the random variable ( boldsymbol{X} ) ? Find mean, variance and standard deviation of ( boldsymbol{X} ) | 12 |

159 | An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01,0.03 and 0.15 respectively. One of the insured person meets with an accident. What is the probability that he is a scooter driver? | 12 |

160 | ( A ) and ( B ) are events with ( P(A)= ) ( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3} ) Find the probability that i) A does not occur ii) neither A nor B occurs | 12 |

161 | A game of numbers has cards marked from ( 11,12,13, ldots, 40 . ) One card is drawn at random. Find the probability that the number drawn is divisible by 7 | 12 |

162 | Two players ( A ) and ( B ) are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that ( A ) and ( B ) give the correct answer are ( alpha ) and ( beta ) respectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if B answers the first question. A ( cdot frac{alpha}{1-(1-alpha)(1-beta)} ) в. ( frac{(1-beta)}{1-(alpha)(beta)} ) c. ( frac{(1-beta) alpha}{1-(1-alpha)(1-beta)} ) D. none of these | 12 |

163 | 31. For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) =P(Exactly one of C or A occurs) = – and P(All the three events occur simultaneously) = 16 Then the probability that at least one of the eve occurs, is: [JEE M 2017) 16 | 11 |

164 | 50 plants were planted each school out of 10 schools. After a month, the number of planets that survived are given below:Find Mean and Variance school [ 2 ] Number of planet 35 survived | 12 |

165 | The queen king,jack of diamonds are removed from a deck of 52 playing cards. One card is drawn. Find the probability of getting a card of (i) a diamond (ii) a jack | 12 |

166 | Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success. | 12 |

167 | Coloured balls are distributed in 3 bags. ( boldsymbol{B}_{1} rightarrow mathbf{1} boldsymbol{B}, mathbf{2} boldsymbol{W}, mathbf{3} boldsymbol{R} ) ( B_{2} rightarrow 2 B, 4 W, 1 R ) ( boldsymbol{B}_{3} rightarrow mathbf{4} boldsymbol{B}, mathbf{5} boldsymbol{W}, mathbf{5} boldsymbol{R} ) A bag is selected at random and then 2 balls are drawn from the selected bag. They happen to be black and red. What is the probability that the balls come from bag 1? | 12 |

168 | If ( boldsymbol{P}(boldsymbol{A})=boldsymbol{P}(boldsymbol{B}), ) then the two events ( boldsymbol{A} ) and ( B ) are – A. Independent B. Dependent c. Equally likely D. Both (A) and (C) | 12 |

169 | If ( P(E)=0.05, ) what is the probability of “not E” ? | 12 |

170 | Roll a die ten times and record the outcomes in the form of table. | 12 |

171 | ( A ) and ( B ) are two independent events such that ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right)=frac{1}{6} ) and ( Pleft(A^{prime}right)=frac{5}{24} . ) Then ( P(B) ) is equal to ( A cdot frac{4}{5} ) B. ( c cdot frac{1}{5} ) D. | 12 |

172 | The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is [2004] 219 128 37 256 256 256 | 12 |

173 | A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events: ( A= ) Both numbers are odd ( B= ) Both numbers are even ( C= ) Sum of the numbers is less than 6 Also, Find ( boldsymbol{A} cup boldsymbol{B}, boldsymbol{A} cap boldsymbol{B}, boldsymbol{A} cup boldsymbol{C}, boldsymbol{A} cap boldsymbol{C} ) Which pairs of events are mutually exclusive | 12 |

174 | 23. IF C and 23. – If C and D are two events such that then the correct statement among the follo (a) P(CD) 2 PC) b) P(CD)<P(C) ents such that C C D and P(D) 0, among the following is [2011] (c) P(CD)= (d) P(CD)=P(C) P(C) | 12 |

175 | A ball is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. The probability of a ball drawn is red, white or blue ( ldots ) A ( cdot frac{1}{3} ) B. ( frac{3}{5} ) ( c cdot frac{2}{3} ) D. ( frac{4}{5} ) | 12 |

176 | Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 2 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 8} ) | 12 |

177 | If ( P(E)=0 ) Then ( P(text { not } E) ) is A . 1 B. – – ( c cdot 0 ) D. ( 1 / 2 ) | 12 |

178 | A box contains 100 tickets numbered ( 1,2,3, dots, 100 . ) two tickets are chosen at random. If it is given that the maximum number on the two chosen tickets is not more than 10 , then the probability that the minimum number on them is not less than 5 is A ( cdot frac{1}{3} ) B. ( frac{1}{5} ) c. ( frac{152}{165} ) D. None of these | 12 |

179 | The probability that atleast one of the events ( A, B ) happens is ( 0.6 . ) If probability of their simultaneously happening is ( 0.5, ) then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= ) A . 0.4 B. 0.8 c. 0.9 D. 1. | 12 |

180 | 13. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (i) red (ü) not black. | 11 |

181 | Suppose that the reliability of a HIV test is specified as follows:Of people having HIV, ( 90 % ) of the test detect the disease but ( 10 % ) go undetected. Of people free of ( mathrm{HIV}, 99 % ) of the test are judged HIV-ive but ( 1 % ) are diagnosed as showing HIV+ive. From a large population of which only ( 0.1 % ) have ( mathrm{HIV} ), one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the person actually has HIV? | 12 |

182 | ales порошо ер 11. What is the probability of choosing a vowel from the alphabets? T oboplonlu out of 5 students can partioint 1 | 11 |

183 | If the difference between the mean and variance of a binomial distribution for 5 trials is ( frac{5}{9}, ) then the distribution is ( ^{A} cdotleft(frac{1}{9}+frac{2}{9}right)^{5} ) ( ^{mathrm{B}}left(frac{1}{4}+frac{3}{4}right)^{5} ) ( ^{c}left(frac{2}{3}+frac{1}{3}right)^{5} ) ( ^{mathrm{D}}left(frac{3}{4}+frac{1}{4}right)^{5} ) | 12 |

184 | If ( P(A)=frac{3}{5} ) and ( P(B)=frac{1}{5}, ) find ( mathbf{1 0 0} boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) if ( boldsymbol{A} ) and ( boldsymbol{B} ) are independent events. | 12 |

185 | There are 2 red and 2 yellow flowers in a basket. A child picks up at random three flowers. What is the probability of picking up both the yellow flowers? | 12 |

186 | In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and Mathematics. How many teach physics? | 12 |

187 | ( A ) and ( B ) two events such that ( P(A cap ) ( left.boldsymbol{B}^{prime}right)=mathbf{0 . 2 0}, boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}right)=mathbf{0 . 1 5}, ) and ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right)=mathbf{0 . 1 0}, ) then ( boldsymbol{p}(boldsymbol{A} / boldsymbol{B}) ) is This question has multiple correct options ( ^{mathbf{A}} cdot P(A mid B)=frac{2}{5} ) в. ( P(A)=0.3 ) c. ( P(A cup B)=0.45 ) D. ( P(B mid A)=frac{1}{3} ) | 12 |

188 | In throwing of a die, let ( A ) be the event ‘an odd humber turns up’, ( B ) be the event ‘a number divisible by 3 turns up’ and ( C ) be the event ‘a number ( leq 4 ) turns up’, Then find the probability that exactly two of ( A, B ) and ( C ) occur. A ( cdot frac{2}{3} ) B. ( frac{1}{6} ) ( c cdot frac{1}{3} ) D. | 12 |

189 | A signal which can be green or red with probability ( frac{4}{5} ) and ( frac{1}{5}, ) respectively, is received at station ( A ) and then transmitted to station B. The probability of each station receiving the signal correctly is ( frac{3}{4} . ) If the signal received at station B is green, then the probability that the original signal was green is ( A cdot frac{3}{5} ) B. ( frac{6}{7} ) c. ( frac{20}{23} ) D. ( frac{9}{20} ) | 12 |

190 | Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the Probability that both are king. | 12 |

191 | A letter is chosen at random from the letters of the English alphabet The probability that it is not a vowel is A . 5/26 B. 21/26 c. ( 15 / 26 ) D. ( 1 / 2 ) | 12 |

192 | One hundred identical coins, each with probability, ( p, ) of showing up heads are tossed once. If ( 0<p<1 ) and the probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of ( p ) is : A . ( 1 / 2 ) B . ( 49 / 101 ) c. ( 50 / 101 ) D. ( 51 / 101 ) | 12 |

193 | State true or false A probability experiment was conducted. Following number is considered as a probability of an outcome? ( mathbf{1 . 4 5} ) A. True B. False | 12 |

194 | Cards marked with numbers 4 to 99 are placed in a box and mixed thoughtly. One card is drawn from this box. Find the probability that the number on the card is a prime number less than 30 | 12 |

195 | If ( P(n) ) is the statement ( ^{prime prime} n^{2} ) is even” then what is ( boldsymbol{P}(mathbf{9}) ) ? | 12 |

196 | A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, then the probability that either both are apples or both are ( operatorname{good} ) is ( frac{316}{435} ) A. True B. False | 12 |

197 | A bag contains 8 black and 5 white balls. 2 balls are drawn. Find the probability that both the balls are white. | 12 |

198 | Tne probability that Krishna will be alive 10 years is ( frac{7}{15} ) and that Hari will be alive is ( frac{7}{10} . ) The probability that both Krishna and Hari will be dead is – A ( cdot frac{21}{150} ) B. ( frac{24}{150} ) ( mathbf{c} cdot frac{49}{150} ) D. ( frac{56}{150} ) | 12 |

199 | (d) 1 A student appears for tes successful if he passes eit III. The probabilities o pears for tests I, II and III. The student is fiul if he passes either in tests I and II or tests I and habilities of the student passing in tests I, II and I are p, q and respectively. If the probability that the student is successful is -, then (1986 – 2 Marks) (a) p=q=1 (b) p=9= (d) p= (©) p=1,q=0 (e) none of these | 12 |

200 | IfE and Fare independent events such that 0<P(E) <1 and 0<P(F)< 1, then (1989 – 2 Marks) (a) E and Fare mutually exclusive (6) E and FC (the complement of the event F) are independent © E and FC are independent ) P(E|F) + P(E|F)=1. 1 Dinle | 12 |

201 | A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied. Each Year-III’s name is placed in the lottery 3 times; each Year-II’s name, 2 times and Year-l’s name, 1 time. What is the probability that a Year-III’s name will be chosen? ( A cdot ) B. ( c cdot frac{3}{3} ) ( D ) | 12 |

202 | Let ( boldsymbol{E} ) and ( boldsymbol{F} ) be two independent events. The probability that both ( boldsymbol{E} ) and ( boldsymbol{F} ) happens is ( 1 / 6 ) and the probability that neither ( boldsymbol{E} ) nor ( boldsymbol{F} ) happens is ( mathbf{1} / mathbf{3} ). Then This question has multiple correct options A ( cdot P(E)=1 / 2, P(F)=1 / 3 ) B . ( P(E)=1 / 2, P(F)=1 / 6 ) C ( cdot P(E)=1 / 6, P(F)=1 / 2 ) D cdot ( P(E)=1 / 3, P(F)=1 / 2 ) | 12 |

203 | 25. Four fair dice D2,D , Dą and Di; each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that DA shows a number appearing on one of D1, D2 and D3 is (2012 91 216 (a) 108 (b) 216 125 (©) 216 127 (d) 216 1 1 .1 | 11 |

204 | ( A ) and ( B ) are two events on a sample space ( S ) such that ( P(A)=0.8, P(B)= ) ( mathbf{0 . 6} ) and ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 9} ) find ( (boldsymbol{A} cap boldsymbol{B}) ) A . 0.3 B. 0.4 ( c cdot 0.5 ) D. 0.6 | 12 |

205 | In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7 . | 12 |

206 | If ( A ) and ( B ) are two events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{1} / 2 ) and ( boldsymbol{P}(boldsymbol{B})=2 / 3, ) then This question has multiple correct options A. ( P(A cup B) geq 2 / 3 ) B . ( Pleft(A cap B^{prime}right) leq 2 / 3 ) c. ( 1 / 6 leq P(A cap B) leq 1 / 2 ) D. ( 1 / 6 leq Pleft(A^{prime} cap Bright) leq 1 / 2 ) | 12 |

207 | An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered ( 2,3,4, dots . .12 ) is picked and the number on the card is noted. The probability that the noted number is either 7 and 8 is ( 1 k 3 / 792 ),where ( k ) is ten’s place of the number ( 1 k 3 . ) F ind the value of ( k .{1 k 3=100+10 times k+3} ) | 12 |

208 | ( 10 % ) of the tools produced by a machine are defective. Find the probability distribution of the number of defective tools when 3 tools are drawn one by one with replacement. | 12 |

209 | In a binomial distribution ( Bleft(n, p=frac{1}{4}right) ) if the probability of at least one success is greater than or equal to ( frac{9}{10}, ) then ( n ) is greater than A ( cdot frac{1}{log _{10} 4+log _{10} 3} ) В. ( frac{9}{log _{10} 4-log _{10} 3} ) c. ( frac{4}{log _{10} 4-log _{10} 3} ) D. ( frac{1}{log _{10} 4-log _{10} 3} ) | 12 |

210 | For a random experiment, all possible outcomes are called A. numerical space. B. event space c. sample space. D. both b and c | 12 |

211 | The probability that there would be 1,2 or 3 persons riding a bicycle are 0.85,0.12 and 0.03 respectively. The expected number of persons per bicycle is A . 2 B. c. 1.18 D. 3 | 12 |

212 | A box contains 6 green balls, 4 blue balls and 5 yellow balls. A ball is drawn at random. Find the probability of (a) Getting a yellow ball. (b) Not getting a green ball. A ( cdot frac{1}{5}, frac{1}{3} ) в. ( frac{4}{15}, frac{3}{15} ) c. ( frac{1}{3}, frac{3}{5} ) D. ( frac{2}{3}, frac{1}{15} ) | 12 |

213 | In a multiple choice question, there are four alternative answer of which one or more than one is correct. A candidate will get marks on the question only if he ticks all the correct answer. The candidate decides to tick all the correct answer. The candidate decides to tick answers at random. If he is allowed up to three chances to answer the question, the probability that he will get marks on it is ( A cdot frac{1}{2} ) B. ( c cdot frac{1}{4} ) D. 5 | 12 |

214 | Suppose ( n(geq 3) ) persons are sitting in row. Two of them are selected at random. The probability that they are not together is A ( cdot 1-frac{2}{n} ) в. ( frac{2}{n-1} ) c. ( _{1-frac{1}{n}} ) D. None of these | 12 |

215 | The marks secured by 400 students in a Mathematics test were normally distributed with mean ( 65 . ) If 120 students got marks above 85 , the number of students securing marks between 45 and 65 is A . 120 B . 20 c. 80 D. 160 | 12 |

216 | If ( A ) and ( B ) are two events, then which of the following does not represent the probability of at most one of ( A, B ) occurs. ( mathbf{A} cdot 1-P(A cap B) ) B . ( P(bar{A})-P(bar{B})+-P(bar{A}+bar{B}) ) ( mathbf{c} cdot P(bar{A})+P(bar{B})+-P(bar{A} cap bar{B}) ) ( mathbf{D} cdot P(A cap bar{B})+P(bar{A} cap bar{B})-P(bar{A} cap bar{B}) ) | 12 |

217 | A coin is tossed for 50 times and get a head 10 times, this action is called A. space B. experiment c. sample D. event | 12 |

218 | Only tenth-, eleventh-, and twelfth- grade students attend Washington High School. The ratio of tenth graders to the school’s total student population is 86: ( 255, ) and the ratio of eleventh graders to the school’s total student population is ( 18: 51 . ) If a student is selected at random from the entire school, the grade in which the student is most likely to be is: A. Tenth B. Eleventh c. Twelfth D. All grades are equally likely E. Cannot be determined from the given information | 12 |

219 | A bag ( A ) contains 2 white and 3 red balls and a bag ( B ) contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from ( operatorname{bag} B ) is ( frac{25}{X}, ) then find the value of ( X ) | 12 |

220 | A random variable ( X ) has the following probability distribution: [ begin{array}{lllll} boldsymbol{X} & 0 & 1 & 2 & 3 \ P(X= & frac{1}{4} & 2 a & 3 a & 4 a end{array} ] Then ( P(1 leq X leq 4) ) is: A. ( frac{10}{21} ) в. c. ( frac{1}{14} ) D. | 12 |

221 | Two dice are thrown simultaneously. If ( X ) denotes the number of sixes, find the expectation of ( boldsymbol{X} ) | 12 |

222 | A parents has two children. If one of them is boy, then the probability that other is, also a boy, is A ( cdot frac{1}{2} ) B. ( frac{1}{4} ) ( c cdot frac{1}{3} ) D. None of these | 12 |

223 | The scores on standardized admissions test are normally distributed with a mean of 500 and a standard deviation of ( 100 . ) What is the probability that a randomly selected student will score between 400 and 600 on the test? A. About ( 63 % ) B. About ( 65 % ) c. About ( 68 % ) D. About ( 70 % ) | 12 |

224 | A bag contains 4 blue, 5 red and 7 green balls. If 4 balls are drawn one by one with replacement, what is the probability that all are blue? A ( cdot frac{1}{16} ) в. c. ( frac{1}{256} ) D. ( frac{1}{64} ) | 12 |

225 | Two coins are tossed simultaneously. Write the sample space ( ^{prime} S^{prime} ) and the number of sample point ( n(S) . A ) is the event of getting no head. Write the event ( A ) in set notation and find ( n(A) ) | 12 |

226 | An urn contains 10 balls coloured either black or red When selecting two balls from the urn at random, the probability that a ball of each color is selected is ( 8 / 15 . ) Assuming that the urn contains more black balls then red balls, the probability that at least one black ball is selected, when selecting two balls, is ( mathbf{A} cdot frac{18}{45} ) B. ( frac{30}{45} ) c. ( frac{39}{45} ) D. ( frac{41}{45} ) | 12 |

227 | OOOOOOO 10. An unbiased die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is then: (1993 – 1 Mark) (a) 16/81 (b) 1/81 (c) 80/81 (d) 65/81 | 11 |

228 | In a bag there are 6 white and 4 black balls. Two balls are drawn one after another without replacement.ff the 1 st ball is known to be white, the probability that the 2 nd ball drawn is also white is ( A cdot frac{2}{9} ) в. ( frac{5}{9} ) ( c cdot frac{8}{9} ) D. ( frac{8}{13} ) | 12 |

229 | In a two child family, one child is a boy. What is the probability that the other child is a girl? | 12 |

230 | If ( A ) and ( B ) are two events, then which of the following does not represent the probability that exactly one of ( A, B ) occurs is This question has multiple correct options ( mathbf{A} cdot P(A)+P(B)-P(A cap B) ) B ( cdot Pleft(A cap B^{prime}right)+Pleft(A^{prime} cap Bright) ) ( mathbf{c} cdot Pleft(A^{prime}right)+Pleft(B^{prime}right)-2 Pleft(A^{prime} cap B^{prime}right) ) D ( . P(A)+P(B)-2 P(A cap B) ) | 12 |

231 | Two numbers are selected at random from the number ( 1,2, ldots, n . ) Let ( p ) denote the probability that the difference between the first and second is not less than ( m ) (where ( 0<m<n ) ). If ( n=25 ) and ( boldsymbol{m}=mathbf{1 0}, ) find ( mathbf{5} boldsymbol{p} ) | 12 |

232 | Consider the following events for a family with children [ A={o f text { both sexes }} ; B= ] ( {a t text { most one boy }} ) In which of the following (are/is) the events ( A ) and ( B ) are independent (a)If a family has 3 children (b) If a family has 2 children Assume that the birth of a boy or a girl is equally likely mutually exclusive and exhaustive | 12 |

233 | An employer sends a letter to his employee but he does not receive the reply (It is certain that employee would have replied if he did receive the letter). It is known that one out of ( n ) letters does not reach its destination. Find the probability that employee does not receive the letter. A ( cdot frac{1}{n-1} ) B. ( frac{n}{2 n-1} ) c. ( frac{n-1}{2 n-1} ) D. ( frac{n-2}{n-1} ) | 12 |

234 | 24. Three numbers are chosen from {1,2,3,..8). The probability that their minimum that their maximum is 6, is: Pers are chosen at random without replacement obability that their minimum is 3, given [2012] | 12 |

235 | Find the chance of throwing more than 15 in one throw with 3 dice. | 12 |

236 | Three unbiased coins are tossed. What is the probability of getting at most two tails or two heads? ( A cdot frac{3}{2} ) B. ( frac{3}{4} ) ( c cdot frac{5}{2} ) D. ( frac{7}{2} ) | 12 |

237 | The least number of times a fair coin is to be tossed in order that the probability of getting atleast one head is at least ( mathbf{0 . 9 9} ) is A . 5 B. 6 ( c cdot 7 ) ( D ) | 12 |

238 | Box I contains 2 white and 3 red balls and box II contains 4 white and 5 red balls. One ball is drawn at random from one of the boxes and is found to be red. Then, the probability that it was from box ( | ), is? ( ^{mathrm{A}} cdot frac{54}{44} ) в. ( frac{54}{14} ) c. ( frac{54}{104} ) D. None of these | 12 |

239 | Three balls are drawn at random from a collection of 7 white, 12 green and 4 red balls. The probability that each is different colour is A ( cdot frac{48}{253} ) в. ( frac{64}{253} ) c. ( frac{23}{253} ) D. ( frac{56}{253} ) | 12 |

240 | 25. A multinta has three alternative answers of which on has 5 questions. Each question ve answers of which exactly one is correct. dent will get 4 or more correct [JEE M 2013] answers just by guessing is: 10 | 12 |

241 | A coin is tossed repeatedly until it shows head. Let ( X ) be the number of tosses required to get head. Write the probability distribution of ( boldsymbol{X} ) | 12 |

242 | Let ( omega ) be a complex cube root of unity with ( omega neq 1 . ) A fair die is thrown three times. If ( r_{1}, r_{2} ) and ( r_{3} ) are the numbers obtained on the die then the probability that ( omega^{r_{1}}+omega^{r_{2}}+omega^{r_{3}}=mathbf{0} ) is A ( cdot frac{1}{18} ) в. ( frac{1}{9} ) ( c cdot frac{2}{9} ) D. ( frac{1}{36} ) | 12 |

243 | State the following statement is true or false The probability of an event can be greater than one also. A. True B. False | 12 |

244 | Given that she is successful, the chance she studied for 4 hours, is A ( cdot frac{6}{12} ) в. ( frac{7}{12} ) c. ( frac{8}{12} ) D. ( frac{9}{12} ) | 12 |

245 | A card is thrown from a pack of 52 cards so that each cards equally likely to be selected. Determine whether in the following case are the events ( A ) and ( B ) independent. ( A= ) the card is drawn is a spade, ( B= ) the card is drawn in an ace. | 12 |

246 | A letter is known to have come form TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is A ( cdot frac{4}{11} ) в. ( frac{7}{11} ) c. ( frac{1}{22} ) D. ( frac{21}{22} ) | 12 |

247 | An experiment is known to be random if the results of the experiment. A. cannot be predicted B. Can be predicted c. can be split into further experiments D. can be selected at random | 12 |

248 | There is ( 30 % ) chance that it rains on any particular day. Given that there is at least one rainy day in a week, what is the probability that there are at least two rainy days in the week? A ( frac{1-4(0.7)^{7}}{1-(0.7)^{7}} ) В. ( frac{4(0.7)^{7}}{1-(0.7)^{7}} ) c. ( frac{1-(0.7)^{7}}{1-4 .(0.7)^{7}} ) D. ( frac{(0.7)^{7}}{1-4 .(0.7)^{7}} ) | 12 |

249 | A is known to speak truth 5 out of 7 times. What is the probability that ( boldsymbol{A} ) reports that it is a 7 when a die is thrown? | 12 |

250 | There are ( 6 % ) defective items in a large bulk of items. Probability that a sample of 8 items will include not more than one defective items is ( 1.42 times(0.94)^{x} ) What is the value of ( x ) | 12 |

251 | If the integers ( m ) and ( n ) are chosen at random from 1 to 100 , then the probability that a number of the form ( 7^{m}+7^{n} ) is divisible by 5 is A ( cdot frac{1}{5} ) B. ( frac{1}{7} ) ( c cdot frac{1}{4} ) D. ( frac{1}{49} ) | 12 |

252 | A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green? A . ( 19 / 20 ) B. 17/20 ( c cdot 8 / 10 ) D. 21/40 ( E cdot 15 / 40 ) | 12 |

253 | The probabilites of three events ( boldsymbol{A}, boldsymbol{B} ) and ( C ) are ( P(A)=0.6, P(B)=0.4 ) and ( boldsymbol{P}(boldsymbol{C})=mathbf{0 . 5 .} ). If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) ( mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})= ) 0.2 and ( P(A cup B cup C) geq 0.85, ) then A ( cdot 0.2 leq P(B cap C) leq 0.35 ) B . ( 0.5 leq P(B cap C) leq 0.85 ) c. ( 0.1 leq P(B cap C) leq 0.35 ) D. None of these | 12 |

254 | Let ( A ) and ( B ) be two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{mathbf{7}}{mathbf{1 0}} ) Then ( P(bar{B}) ) is equal to A ( cdot frac{3}{8} ) B. ( frac{2}{7} ) ( c cdot frac{7}{9} ) D. none of these | 12 |

255 | For two events ( A ) and ( B ) with ( P(B) neq 1 ) prove that ( boldsymbol{P}left(boldsymbol{A} mid boldsymbol{B}^{prime}right)= ) ( frac{boldsymbol{P}(boldsymbol{A})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{1-boldsymbol{P}(boldsymbol{B})} ) | 12 |

256 | An electric component manufactured by ‘RASU Electronics’ is tested for its defectiveness by a sophisticated testing device. Let ( A ) denote the event “the device is defective” and ( B ) the event “the testing device reveals the component to be defective”. Suppose ( boldsymbol{P}(boldsymbol{A})=boldsymbol{alpha} ) and ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A})=boldsymbol{P}left(boldsymbol{B}^{prime} mid boldsymbol{A}^{prime}right)= ) ( mathbf{1}-boldsymbol{alpha}, ) where ( mathbf{0}<boldsymbol{alpha}<mathbf{1}, ) then This question has multiple correct options ( mathbf{A} cdot P(B)=2 alpha(1-alpha) ) B . ( Pleft(A mid B^{prime}right)=1 / 2 ) C ( cdot Pleft(B^{prime}right)=(1-alpha)^{2} ) D ( cdot Pleft(A^{prime} mid B^{prime}right)=[alpha /(1-alpha)]^{2} ) | 12 |

257 | UMU U UUvVpliv UVAUVA 13. A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals (1998 – 2 Marks) (a) 1/2 (b) 1/32 (0) 31/32 (d) 175 | 12 |

258 | Rajdhani Express stops at six intermediate stations between Kota and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is ( ^{A} cdot frac{^{6} P_{5}}{6^{5}} ) в. ( frac{^{6} C_{5}}{6^{5}} ) c. ( frac{7}{7^{5}} ) D. ( frac{7}{7^{5}} ) | 12 |

259 | Cards marked with the numbers 2 to 101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is an even prime number less than 16 . A ( cdot frac{5}{28} ) B. ( frac{3}{50} ) ( c cdot frac{3}{25} ) D. ( frac{1}{100} ) | 12 |

260 | There are 3 bags each containing 5 white balls and 2 black balls and 2 bags each containing 1 white balls and 4 black balls, a black ball having been drawn, find the chance that it came from the first group. A ( cdot frac{28}{43} ) в. ( frac{15}{43} ) c. ( frac{15}{28} ) D. ( frac{13}{28} ) | 12 |

261 | A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is. ( ^{A} cdotleft(frac{1}{10}right)^{5} ) B. ( left(frac{1}{2}right)^{5} ) ( ^{mathbf{c}} cdotleft(frac{9}{10}right) ) D. ( left(frac{9}{10}right)^{5} ) | 12 |

262 | A fair coin is tossed 99 times. Let ( X ) be the number of times heads occurs. Then ( P(X=r) ) is maximum when ( r ) is A . 49 B. 52 ( c .51 ) D. None of these | 12 |

263 | When a die is thrown, list the number of outcomes of an event of getting a number greater than 5 | 12 |

264 | Let ( mathbf{x}=mathbf{3}^{mathbf{n}} . ) The index ‘n’ is given a positive integral value at random. The probability that the value of ‘x’ will have 3 in the units place is A . ( 1 / 4 ) B. ( 1 / 2 ) c. ( 1 / 3 ) D. ( 1 / 5 ) | 12 |

265 | The letters of the work “Questions” are arranged in a row at random.The probability that there are exactly two letters between ( Q ) and ( S ) is. A ( cdot frac{1}{14} ) B. ( frac{5}{7} ) ( c cdot frac{1}{7} ) D. ( frac{5}{28} ) | 12 |

266 | In a class of 75 students, 15 are above average, 45 are average and the rest below average achievers. The probability that an above average achieving student fails is ( 0.005, ) that an average achieving student fails is 0.05 and the probability of a below average achieving student failing is ( 0.15 . ) If ( a ) student is know to have passed, what is the probability that he is a below average achiever? | 12 |

267 | A bag contains ( (2 n+1) ) coins. It is known that ( n ) of these coins have a head on both sides, whereas the remaining ( n+1 ) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is ( frac{31}{42}, ) then ( n ) is equal to A . 10 B. 11 c. 12 D. 13 | 12 |

268 | The probabilities that three men hit a target are ( 1 / 6,1 / 4 ) and ( 1 / 3 . ) Each man shoots once at the target. What is the probability that exactly one of them hits the target? A ( cdot 11 / 72 ) B. 21/72 c. ( 31 / 72 ) D. 3/4 | 12 |

269 | How many play hockey only? | 12 |

270 | A die is thrown. Write the sample space. If ( P ) is the event of getting an odd number, then write the event ( P ) using set notation. | 12 |

271 | If ( P(A)=0, ) then the event ( A ) A. Will never happen B. Will always happen c. May happen D. May not happen | 12 |

272 | IF ( P(A)=frac{1}{3}, P(B)=frac{1}{12} ) and ( P(A r ) ( B)=frac{1}{36}, ) are the events ( A ) and ( B ) independent? | 12 |

273 | If ( mathbf{A} ) and ( mathbf{B} ) are two events such that ( mathbf{P}(mathbf{A})=frac{mathbf{3}}{mathbf{4}} ) and ( mathbf{P}(mathbf{B})=frac{mathbf{5}}{8}, ) then This question has multiple correct options A ( cdot 1 geq P(A cup B) geq frac{3}{4} ) в. ( Pleft(A^{prime} cup Bright) leq frac{1}{4} ) c. ( frac{3}{8} leq P(mathrm{A} cap B) leq frac{5}{8} ) D. ( frac{1}{8} leq Pleft(A cap B^{prime}right) leq frac{3}{8} ) | 12 |

274 | Cards marked with the numbers 2 to 101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a perfect square. A ( cdot frac{9}{100} ) в. ( frac{5}{100} ) c. ( frac{4}{100} ) D. ( frac{7}{100} ) | 12 |

275 | A die is thrown. Find the probability of getting: 2 or 4 | 12 |

276 | Drawing 4 queen cards from a well- shuffled deck of 52 cards. This activity is called an A. measurement B. experiment c. event D. sample | 12 |

277 | An integer is chosen at random between 1 and ( 100 . ) Find the probability that it is divisible by 8 is ( frac{m}{25} . ) Find ( m ) | 12 |

278 | Two dice are thrown. The events ( A, B ) and ( C ) are as follows: A : getting an even number on the first die B : getting an odd number on the first die C : getting the sum of the numbers on the dice ( leq 5 ) State true or false : (give reason for your answer) | 12 |

279 | If ( P(A)=frac{1}{8} ) and ( P(B)=frac{5}{8} . ) Which of the following statements is correct? A ( cdot P(A cup B) leq frac{3}{4} ) B ( cdot P(A cap B) leq frac{5}{8} ) ( mathbf{c} cdot P(bar{A} cap B) leq frac{5}{8} ) D ( cdot P(A cap B) geq frac{5}{8} ) | 12 |

280 | In which experiment outcomes are not predictable? A. sample B. event c. random D. essential | 12 |

281 | If in ( Q .104, ) we are told that a white ball has been drawn, find the probability that it was drawn from the first urn. ( ^{A} cdot frac{5}{9} ) в. ( frac{2}{3} ) c. ( frac{2}{9} ) D. ( frac{7}{9} ) | 12 |

282 | Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of ( 100 . ) Tom wants to be admitted to this university and he knows that he must score better than at least ( 70 % ) of the students who took the test. Tom takes the test and scores 585 Tom does better than what percentage of students? A. ( 89.23 % ) B. ( 77.26 % ) c. ( 70.23 % ) D. ( 80.23 % ) | 12 |

283 | From a pack of cards two are accidentally dropped probability they are of opposite shade is A ( cdot frac{13}{51} ) в. ( frac{1}{52 times 51} ) c. ( frac{26}{51} ) D. None of these | 12 |

284 | A coin is tossed three times, where (i) ( E: ) head on third toss, ( F: ) heads on first two tosses (ii) ( E: ) at least two heads, ( F: ) at most two heads (iii) ( E: ) at most two tails, ( F: ) at least one tail. | 12 |

285 | 26. Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is (JEE Adv. 2014) | 11 |

286 | An urn contains five balls alike in every respect save colour. If three of these balls are white and two are black and we draw two balls at random from this urn without replacing them. If A is the event that the first ball drawn is white and ( mathrm{B} ) the event that the second ball drawn is black, are ( A ) and ( B ) independent? If ( A ) and ( B ) are independent then enter 1 , else enter 0 . | 12 |

287 | Only one subject A ( cdot frac{14}{25} ) в. ( frac{11}{25} ) c. ( frac{13}{25} ) D. ( frac{12}{25} ) | 12 |

288 | In a class there are 14 boys and 10 girls If one child is absent the probability that it is a boy is A ( cdot frac{5}{12} ) в. ( frac{7}{12} ) c. ( frac{10}{14} ) D. | 12 |

289 | If Republic Day falls on Friday this year and Shyam was born on 4 days before 12th January, then he celebrates his birthday on A. Tuesday B. Sunday c. Monday D. wednesday | 12 |

290 | An experiment can result in only 3 mutually exclusive events ( A, B ) and ( C ) If ( boldsymbol{P}(boldsymbol{A})=mathbf{2} boldsymbol{P}(boldsymbol{B})=mathbf{3} boldsymbol{P}(boldsymbol{C}), ) then ( boldsymbol{P}(boldsymbol{A})= ) ( A cdot frac{6}{11} ) B. ( frac{5}{11} ) ( c cdot frac{9}{11} ) D. None | 12 |

291 | Two small square on a chess board are chosen at random. Probability that they have a common side is A ( cdot frac{1}{3} ) в. ( frac{1}{9} ) c. ( frac{1}{18} ) D. None of these | 12 |

292 | State and prove Baye’s theorem. | 12 |

293 | In a bolt factory, three machines ( A, B ) and ( C ) manufacture ( 25 %, 35 % ) and ( 40 % ) of the total production respectively. Of their respective outputs, ( 5 %, 4 % ) and ( 2 % ) are defective. A bolt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine ( C ) | 12 |

294 | Find the binomial distribution for which the mean is 4 and variance 3 | 12 |

295 | 28. Let two fair six-faced dice A and B be thro If E, is the event that die A shows up that die B shows up two and Ez is the numbers on both dice is odd, then w statements is NOT true? (a) E, and E, are independent. (b) E,, E, and E, are independent. (c) E, and E, are independent. (d) E, and E, are independent. iced dice A and B be thrown simultaneously. vent that die A shows up four, E, is the event ws up two and E, is the event that the sum of th dice is odd, then which of the following [JEEM 2016 | 12 |

296 | A and B are mutually exclusive events, then ( mathbf{A} cdot P(A) leq P(bar{B}) ) B ( . P(mathrm{A})>P(bar{B}) ) ( mathbf{c} cdot mathrm{P}(mathrm{A})<mathrm{P}(mathrm{B}) ) D. ( P(A)=P(B) ) | 12 |

297 | An article manufactured by a company consists of two parts ( X ) and ( Y . ) In the process of manufacture of the part ( boldsymbol{X} . mathbf{9} ) out of 100 parts may be defective. Similarly 5 out of 100 are likely to be defective in part ( Y ). Calculate the probability that the assembled product will not be defective. | 12 |

298 | When a coin is tossed in an experiment, the result is either a head or a tail. A head is given a point value of 1 and ( a ) tail is given a point value of ( -1 . ) If the sum of the point values after 50 tosses is ( 14, ) how many of the tosses must have resulted in heads? A . 14 B. 18 c. 32 D. 36 E. 39 | 12 |

299 | Two numbers ( X ) and ( Y ) are chosen at random (without replacement) from the ( operatorname{set} 1,2, dots, 5 N . ) The probability that ( X^{n} sim Y^{n} ) is divisible by 5 is A ( frac{N-1}{5 N-1} ) в. ( frac{4(4 N-1)}{5(5 N-1)} ) c. ( frac{17 N-5}{5(5 N-1)} ) D. None of these | 12 |

300 | ( A, B, C ) are pair wise independent. A. True B. False | 12 |

301 | A class consists of 100 students, 25 of them are girls and 75 boys, 20 of them are rich and remaining poor, 40 of them are fair complexioned. The Probability of selecting a fair complexioned rich girl is | 12 |

302 | Out of 50 tickets numbered ( 00,01,02, ldots ., 49 ) one ticket is drawn randomly, the probability of the ticket having the product of its digits 7 given that the sum of the digits is ( 8, ) is A ( cdot frac{1}{14} ) B. ( frac{3}{14} ) ( c cdot frac{1}{5} ) D. None of these | 12 |

303 | 16 5. Events A, B, C are mutually excl e mutually exclusive events such that P(A) = 3x+1, P(B) = 1-* and PCC) – 1-2x The set of possible values of x are in the interval. [2003] (a) [0,1] (b) (a) 53) | 11 |

304 | A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students should fail the test (grades ( < ) 60)( ? ) A . 15.21 в. 23.2 c. ( 15.87 % ) D. 16.23 | 12 |

305 | There are four kinds of trees in an orchard. Four part of total trees are Neem trees. Half of the remaining trees are Mango trees. Half of the remaining trees are Drumstick trees and the remaining 6 trees are Peepel trees. Find the total number of trees in the orchard. | 12 |

306 | Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3 , what is the probability that it is an even number? | 12 |

307 | Three coins are tossed. Describe three events ( A, B ) and ( C ) which are mutually exclusive and exhaustive | 12 |

308 | There are 45 boys and girls in a class. Given the probability that a boy is chosen is ( frac{4}{15} . ) Find the number of girls ( A cdot 8 ) B. 12 c. 25 D. 33 | 12 |

309 | Assertion If ( A, B, C ) are three events such that ( P(A)=frac{1}{4}, P(B)=frac{1}{6} & P(C)=frac{2}{3} ) then events ( A, B, C ) are mutually exclusive. Reason If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})+ ) ( boldsymbol{P}(boldsymbol{C}) ) then ( A, B, C ) are mutually exclusive events. A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

310 | Three coins are tossed once. Let ( boldsymbol{A} ) denote the event ‘three heads show”, ( boldsymbol{B} ) denote the event “two heads and one tail show” ( C ) denote the event “three tails show” and ( D ) denote the event ‘a head shows on the first coin” Which events are (i) mutually exclusive? (ii) simple? (iii) compound? | 12 |

311 | From a pack of 52 playing cards, face cards and tens are removed and kept aside then a card is drawn at random from the remaining cards. If A : The event that the card drawn is an ace ( mathrm{H}: ) The event that the card drawn is a heart S : The event that the card drawn is a spade then which of the following holds? This question has multiple correct options ( mathbf{A} cdot 9 P(A)=4 P(H) ) B . ( P(S)=4 P(A cap H) ) c. ( 3 P(H)=3 P(A cup S) ) D. None of these | 12 |

312 | A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. | 12 |

313 | What is the probability that a two digit number selected at random will be a multiple of 3 and not a multiple of ( 5 ? ) A ( cdot frac{1}{15} ) в. ( frac{3}{15} ) c. ( frac{4}{15} ) D. ( frac{5}{15} ) | 12 |

314 | At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidate who are really capable, ( 80 % ) pass the test and of the incapable, ( 25 % ) pass the test. Given that ( 40 % ) of the candidates are really capable, then the proportion of capable college students is about A . ( 68 % ) B. 70% c. ( 73 % ) D. 75% | 12 |

315 | The mathematical study of randomness is called probability theory. A. True B. False c. Partly true D. None of above | 12 |

316 | The variance of the random variable ( x ) whose probability distribution is given by ( boldsymbol{X}=boldsymbol{x}: quad mathbf{0} quad mathbf{1} quad mathbf{2} quad mathbf{3} ) ( boldsymbol{p}(boldsymbol{X}=boldsymbol{x}): quad frac{1}{3} frac{1}{2} boldsymbol{0} frac{1}{boldsymbol{6}} ) A . 0.5 B. 1 ( c .1 .5 ) D. 2.0 | 12 |

317 | An article manufactured by a company consists of two parts ( X ) and ( Y . ) In the process of manufacture of the part ( boldsymbol{X} . mathbf{9} ) out of 100 parts may be defective. Similarly 5 out of 100 are likely to be defective in part ( Y ). Calculate the probability that the assembled product will not be defective. | 12 |

318 | 5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that there are exactly 3 hearts is A. ( frac{13}{^{13} s_{3}+^{13} c_{4}+^{13} c_{5}} ) в. ( c ) D. ( frac{13}{^{13} s_{3} times^{13} c_{4} times^{13} c_{5}} ) | 12 |

319 | For any two events ( A ) and ( B ) ( mathbf{A} cdot P(A)+P(B)>P(A cap B) ) B ( cdot P(A)+P(B)<P(A cap B) ) ( mathbf{c} cdot P(A)+P(B) geq P(A cap B) ) D ( . P(A) times P(B) leq P(A cap B) ) | 12 |

320 | A bag contains 25 tickets, numbered from 1 to ( 25 . ) A ticket is drawn at random. Find the probability that the ticket will show even number. | 12 |

321 | Define probability of an event? | 12 |

322 | The probability that a person will get an electric contract is ( frac{2}{5} ) and the probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) what is the probability that he will get both? | 12 |

323 | 17. A ship is fitted with three engines E , E, and Ez . The engines function independently of each other with 1 1 respective probabilities and -. For the ship to be 2 4 4 operational at least two of its engines must function. Let X denote the event that the ship is operational and let X, X, and X, denote respectively the events that the engines E, E, and E, are functioning. Which of the following is(are) true ? (2012) (a) P[xx[x]=1 (b) P [Exactly two engines of the ship are functioning (C) P[X|X2]= (a) P[X]X1] = 16 | 12 |

324 | Following is the distribution function ( (x) ) of a discrete ( r . v . x ) ( F(x) ) begin{tabular}{l} 0.2 \ hline end{tabular} 0.37 ( begin{array}{ll}text { 0.48 } & text { 0.62 }end{array} ) (i) Find the probability distribution of ( x ) (ii) Find ( P(x leq 3),(2<x<5) ) | 12 |

325 | If ( M ) and ( N ) are any two events, the probability that the exactly one of them occurs is This question has multiple correct options A ( cdot P(M)+P(N)-2 P(M cap N) ) B . ( P(M)+P(N)-P(M cap N)^{c} ) ( mathbf{c} cdot Pleft(M^{c}right)+Pleft(N^{c}right)-2 Pleft(M^{c} cap N^{c}right) ) D ( Pleft(M cap N^{c}right)+Pleft(M^{c} cap Nright) ) | 12 |

326 | ff ( x ) follows the Binomial distribution with parameters ( n=6 ) and ( p ) and ( mathbf{9} P(X=4)=P(X=2), ) then ( p ) is A ( cdot frac{1}{4} ) B. ( c cdot frac{1}{2} ) D. ( frac{2}{3} ) | 12 |

327 | If ( A ) and ( B ) are events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) ) | 12 |

328 | A single 6 -sided die is rolled. What is the probability of rolling a 4 on the die? A ( cdot frac{1}{12} ) B. ( frac{2}{3} ) ( c cdot frac{3}{2} ) D. | 12 |

329 | A box contains ( b ) blue balls and ( r ) red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue is A ( cdot frac{b}{r+b} ) в. ( frac{b^{2}}{(r+b)^{2}} ) c. ( frac{b+1}{r+b+1} ) D. ( frac{b(b+1)}{(r+b)(r+b+1)} ) | 12 |

330 | A letter is known to have come either from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or ( boldsymbol{C A L} boldsymbol{C U T T A} ) On the envelope just two consecutive letters ( T A ) are visible. What is the probability that the letter came from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{R} ? ) A ( .1 / 11 ) в. ( 7 / 9 ) c. ( 4 / 11 ) D. ( 7 / 11 ) | 12 |

331 | A bag contains 6 white, 5 black and 4 red balls. Find the probability of getting either a white or a black ball in a single draw. If the answer is ( a / b, ) where HCF of ( a ) and ( b ) is ( 1, ) then find ( b-a ? ) | 12 |

332 | A dice is manufactured in such a way that probability of getting an even number is twice likely to occur as an odd number. If the dice is tossed twice, find the probability distribution of the random variable representing the perfect square in the both tosses. | 12 |

333 | The standard deviation ( sigma ) of ( (q+p)^{16} ) is 2. The mean of the distribution is ( A cdot 2 ) B. 8 c. 16 D. 20 | 12 |

334 | Match the follwoing | 12 |

335 | A purse contains 2 silver and 4 copper coins. ( A ) second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver ( operatorname{coin} ) | 12 |

336 | When two coins are tossed one after another list the outcomes of getting at least one head. ( mathbf{A} cdot{H H} ) в. ( {H T, T H} ) c. ( {T T} ) D. ( {T H, H T, H H} ) | 12 |

337 | A bag contains some white and some black balls, all combinations of balls being equally likely. The total number of balls in the bag is ( 10 . ) If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is A ( cdot frac{14}{55} ) B. ( frac{12}{55} ) c. ( frac{2}{11} ) D. ( frac{8}{55} ) | 12 |

338 | nent from a Two cards are drawn successively with replacement from well-shuffled deck of 52 cards. Let X denote the rande variable of number of aces obtained in the two drawn card Then P(X=1)+P(X=2) equals: JEEM 2019-9 Jan (MI (a) 49/169 (b) 52/169 (c) 24/169 (d) 25/169 | 12 |

339 | Suppose a girl throws a die. If she gets a 5 or ( 6, ) she tosses a coin 3 times and notes the number of heads. If she gets 1,2,3 and 4 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head. What is the probability that she threw 1,2,3 or 4 with the die? | 12 |

340 | Four different objects 1,2,3,4 are distributed at random in four places marked ( 1,2,3,4 . ) What is the probability that none of the objects occupy the place corresponding to their number? A ( cdot frac{17}{24} ) в. ( frac{3}{8} ) c. ( frac{1}{2} ) D. | 12 |

341 | If ( A ) and ( B ) be two events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{1} / mathbf{4}, boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{3} ) and ( boldsymbol{P}(boldsymbol{A} cup ) ( B)=1 / 2 ) show that ( A ) and ( B ) are independence events. | 12 |

342 | Assertion If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})>boldsymbol{P}(boldsymbol{A}) ) then. ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})> ) ( boldsymbol{P}(boldsymbol{B}) ) Reason fevents ( A & B ) are dependent, then ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{B})} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

343 | Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as (i) number greater than 4 (ii) six appears on at least one die | 12 |

344 | Identify and write the like terms in each of the following groups. (i) ( a^{2}, b^{2},-2 a^{2}, c^{2}, 4 a ) A ( cdotleft(a^{6}, 2 a^{2}right)^{2} ) В ( cdotleft(a^{2},-2 a^{2}right) ) ( mathbf{C} cdotleft(a^{3}, 2 a^{2}right) ) D. ( left(a^{2}, 2 a^{3}right) ) | 12 |

345 | Of the students in a school, it is known that ( 30 % ) have ( 100 % ) attendance and 70% students are irregular. Previous year results report that ( 70 % ) of all students who have ( 100 % ) attendance attain A grade and ( 10 % ) irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an ( A ) grade. What is the probability that the student has ( 100 % ) attendance? Is regularity required only in school? Justify your answer. | 12 |

346 | A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of ( 8 ? ) | 12 |

347 | When a die is thrown, list the outcomes of an event of getting: a prime number. A. 2,3,5 в. 1,3,5 c. 3,5,7 D. 1,2,5 | 12 |

348 | If ( A & B ) are two given events, then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) is A. Not less than ( P(A)+P(B)-1 ) B. Not greater than ( P(A)+P(B)-P(A cup B) ) C . Equal to ( P(A)+P(B)+P(A cap B) ) D. Equal to ( P(A)+P(B)+P(A cup B) ) | 12 |

349 | A box contains 100 cards marked with numbers 1 to ( 100 . ) If one card is drawn randomly from the box. Find the probability that it bears. (1) Even prime number. (2) A number divisible by 7. (3) The number at unit place is 9 | 12 |

350 | A card from a pack 52 cards is lost. From the remaining card of the pack, one card is drawn and is found be heart, Find the probability that the lost cards were both hearts. | 12 |

351 | The probability of a leap year having 53 Mondays is: A ( cdot frac{2}{7} ) B. ( frac{1}{7} ) ( c cdot frac{3}{7} ) D. | 12 |

352 | Three men have 6 different trousers, 5 different shirts and 4 different caps. Number of different ways in which they can wear them is | 12 |

353 | A examination consists of 8 questions in each of which one of the 5 alternatives is the correct one. On the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternatives with equal probability, the probability that he gets more than one correct answer is equal to five alternatives with equal probability,the probability that he gets more than one correct answer is equal to A ( cdot(0.8)^{8} ) B. ( 3(0.8)^{8} ) c. ( 1-(0.8)^{8} ) D. ( 1-3(0.8)^{8} ) | 12 |

354 | A coin is tossed three times. Consider the following events: A: No head appears B: Exactly one head appears C: At least two heads appear Which one of the following is correct? A ( .(A cup B) cap(A cup C)=B cup C ) B . ( left(A cap B^{prime}right) cupleft(A cap C^{prime}right)=B^{prime} cup C^{prime} ) C ( . A cap Bleft(B^{prime} cup C^{prime}right)=A cup B cup C ) D. ( A capleft(B^{prime} cup C^{prime}right)=B^{prime} cap C^{prime} ) | 12 |

355 | A pair of fair dice is rolled together till a sum of 7 or 11 is obtained. Let ( p ) denote the probability that 7 comes before 11 Find the value of ( 4 p ) | 12 |

356 | The author of the book “The book on game of chance” based on probability theory is- A. J.Cardon B. R.S.Woodwards c. P.S.Laplace D. P.D.Pherma | 12 |

357 | Kamal and Monika appeared for an interview for two vacancies. The probability of Kamal’s selection is ( frac{1}{3} ) and that of Monika’s selection is ( frac{1}{5} . ) Find the probability that both of them will be selected. | 12 |

358 | Assertion A bag contains ( n+1 ) coins. It is known that one of these coins has a head on both sides while the other coins are fair. One coins is selected at random and tossed. If head turns up, the probability that the selected coin was fair, is ( frac{n}{n+2} ) Reason If an event ( A ) occurs with two mutually | 12 |

359 | The average length of time required to complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 30 and 50 minutes to complete the questionnaire? A. About ( 85 % ) B. About ( 90 % ) c. About ( 95 % ) D. none | 12 |

360 | A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, the probability of at least 5 successes is ( frac{49}{9^{x}} . ) Find the value of ( x ) | 12 |

361 | If ( A ) and ( B ) are any two events such that ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(text {Aand} B)=boldsymbol{P}(boldsymbol{A}) ) then ( mathbf{A} cdot P(B mid A)=1 ) B . ( P(A mid B)=1 ) c. ( P(B mid A)=0 ) D cdot ( P(A mid B)=0 ) | 12 |

362 | Let ( A ) and ( B ) be events such that ( P(A)-frac{1}{6}, P(B)=frac{1}{4} ) and ( P(A cap B)= ) ( frac{1}{12} cdot operatorname{Find} P(B / A) cdot P(A / B) ) | 12 |

363 | If 3 coins are tossed simultaneously, the probability of 1 head and 2 tails is: A ( cdot frac{1}{8} ) в. ( frac{3}{8} ) ( c cdot frac{5}{8} ) D. ( frac{7}{8} ) | 12 |

364 | A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random from the bag is three times that of a red ball, find the number of blue balls in the bag. | 12 |

365 | If ( A ) and ( B ) are events such that ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})=boldsymbol{P}(boldsymbol{B} mid boldsymbol{A}), ) then A ( . A subset B ) but ( A neq B ) в. ( A=B ) c. ( A cap B=Phi ) D ( cdot P(A)=P(B) ) | 12 |

366 | If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{B})=frac{mathbf{1}}{mathbf{5}} ) then A ( cdot P(A cup B)=frac{3}{5} ) в. ( Pleft(frac{A}{B}right)=frac{1}{2} ) ( ^{c} cdot pleft(frac{A}{A cup B}right)=frac{5}{6} ) ( ^{mathrm{D}} cdot_{P}left(frac{A}{bar{A}} stackrel{cap}{longrightarrow} overline{bar{B}}right)=0 ) | 12 |

367 | Of the students in a college, it is known that ( 60 % ) reside in hostel and ( 40 % ) are day scholars (not residing in hostel) Previous year results report that ( 30 % ) of all students who reside in hostel attain ( A ) grade and ( 20 % ) of day scholars attain ( A ) grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an ( A ) grade, what is the probability that the student is a hosteller? | 12 |

368 | A card from pack of 52 cards is lost. From the remaining card of the pack, one card is drawn and is found to be heart, find the probability of missing card to be (I) heart (II) club. | 12 |

369 | A bag contains ( a ) white and ( b ) black balls. Two players, ( A ) and ( B ) alternately draw a ball from the bag, replacing the ball each time after the draw till on of them draws a white ball and win the game. ( A ) begins the game. If the probability of ( boldsymbol{A} ) winning the game is three times that of ( B ), the ratio ( a: b ) is A . 1: 1 B. 1: 2 ( c cdot 2: 1 ) D. None of these | 12 |

370 | 15. A pair of fair dice 0.00 (a) 0.14 air of fair dice is thrown independently three times. The hability of getting a score of exactly 9 twice is [20071 (a) 8/729 (b) 8/243 C ) 1/729 (d) 8/9 is given that the evente | 12 |

371 | A bag contains 6 red balls and 8 green balls. A ball is drawn at random. What is the probability that the ball is green | 12 |

372 | In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. | 12 |

373 | For ( k=1,2,3 ) the box ( B_{k} ) contains ( k ) red balls and ( (k+1) ) white balls, let ( Pleft(B_{1}right)=frac{1}{2}, Pleft(B_{2}right)=1 ) and ( Pleft(B_{3}right)= ) ( frac{1}{6} cdot A ) box is selected at random and ( a ) ball is drawn from it. If a red ball is drawn, then the probability that it has come from box ( B_{2} ) is A ( cdot frac{35}{78} ) в. ( frac{14}{39} ) c. ( frac{10}{13} ) D. ( frac{12}{13} ) | 12 |

374 | 19. Four persons independently solve a certain problem corre with probabilities . Then the probability that the problem is solved correctly by at least one of them is (JEE Adv. 2013) 235 253 256 256 256 | 12 |

375 | The probability that a student entering a university will graduate is ( 0.4 . ) If the probability that out of 3 students of the university, only one will graduate is ( frac{432}{10^{x}} ) then the value of ( x ) is | 12 |

376 | Two independent events are always mutually exclusive, If this is true enter 1, else enter 0 A. True B. False | 12 |

377 | More than 4 on atleast one of the three successive throws, If the answer is ( frac{a}{b} ) where the HCF of ( a ) and ( b ) is 1 , then find ( boldsymbol{b}-boldsymbol{a} ) | 12 |

378 | A coin is tossed 100 times with the following frequencies: Head : 20. Find the probability for event having heads only. A . 0.2 B. 0.5 c. 0.65 D. 1.5 | 12 |

379 | The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is A ( cdot frac{128}{256} ) в. ( frac{219}{256} ) c. ( frac{37}{256} ) D. ( frac{28}{256} ) | 12 |

380 | Rahim takes out all the hearts from the cards. What is the probability of Picking out a diamonds. | 12 |

381 | Let ( u_{1} ) and ( u_{2} ) be two urns such that ( u_{1} ) contains 3 white, 2 red balls and ( u_{2} ) contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn ( u_{1} ) and put into ( u_{2} . ) However, if tail appears, then 2 balls are drawn at random from ( u_{1} ) and put into ( u_{2} . ) Now, 1 ball is drawn at random from ( u_{2} ). Then, probability of the drawn ball from ( u_{2} ) being white is A ( cdot frac{13}{30} ) в. ( frac{23}{30} ) c. ( frac{19}{30} ) D. ( frac{11}{30} ) | 12 |

382 | In which event, the experiment is impossible? A. Tossing a coin for head or tail B. 5 in case of throwing a dice. c. Rolling a dice for 7 D. Tossing a coin to get a tail. | 12 |

383 | Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find ( E(X) ) A ( cdot frac{14}{3} ) B. ( frac{13}{3} ) ( c cdot frac{12}{3} ) D. ( frac{11}{3} ) | 12 |

384 | A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is (1984 – 2 Marks) (a) 5/64 (b) 27/32 (c) 5/32 (d) 1/2 11 ..1: 1 1 airgeab :+ 11:1: af | 12 |

385 | The probability that a person will get an electric contract is ( frac{2}{5} ) and the probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) what is the probability that he will get both? | 12 |

386 | A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number ( 1,2,3, dots .12 ) as shown in Fig. What is the probability that it will point to: (i) 10 (ii) an odd number (iii) a number which is a multiple of 3 (iv) an even number. | 12 |

387 | A player tosses 2 fair coins. He wins Rs5 if 2 heads appear, Rs2 if head appears and Rs1 if no head appears. Find his expected winning amount and variance of winning amount. | 12 |

388 | Three shots are fired at a target in succession. The probabilities of a hit in the first shot is ( frac{1}{2}, ) in the second ( frac{2}{3} ) and in the third shot is ( frac{3}{4}, ) In case of exactly one hit, the probability of destroying the target is ( frac{1}{3} ) and in the case of exactly two hits ( frac{7}{11} ) an in the case of three hits is ( 1.0 . ) Find the probability of destroying the target in three shots ( A cdot 3 ) ( overline{4} ) B. ( frac{3}{8} ) ( c cdot frac{5}{8} ) D. 4 | 12 |

389 | If a coin is tossed, then the probability that a head turns up is A ( cdot frac{1}{2} ) B. ( c cdot frac{1}{3} ) D. ( frac{1}{6} ) | 12 |

390 | Let ( X ) denote the number of hours you study during a randomly selected school day. The probability that ( X ) can take the values of ( x, ) has the following form, where ( k ) is some constant ( boldsymbol{P}(boldsymbol{X}=boldsymbol{x})=left{begin{array}{ll}mathbf{0}, mathbf{1} & text { if } boldsymbol{x}=mathbf{0} \ boldsymbol{K} boldsymbol{x} & text { if } boldsymbol{x}=mathbf{1} text { or } mathbf{2} \ boldsymbol{K}(mathbf{5}-boldsymbol{x}) & text { if } boldsymbol{x}=mathbf{3} text { or } mathbf{4} \ mathbf{0} & text { otherwise }end{array}right. ) What is the probability that you study. For at least two hour. | 12 |

391 | The probability of getting at least a single ( ^{prime} 1^{prime} ) when two dice are rolled is A ( cdot frac{11}{36} ) в. ( frac{25}{36} ) ( c cdot frac{1}{6} ) D. ( frac{1}{8} ) | 12 |

392 | ( operatorname{Let} P(A)=0.4 ) and ( P(A cup B)= ) ( P(A cap B), ) find ( 5 P(B) ) | 12 |

393 | ( A ) speaks the truth ‘3 times out of ( 4^{prime} ) and ( B ) speaks the truth ‘2 times out of 3 ‘, ( A ) die is thrown. Both assert that the number turned up is 2. Find the probability of the truth of their assertion. | 12 |

394 | ( Pleft(frac{B}{A}right) ) is defined only when: A . ( A ) is a sure event B. ( B ) is a sure event c. ( A ) is not an impossible event D. ( B ) is an impossible event | 12 |

395 | If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) then find ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) ) | 12 |

396 | Assume that the chances of a patient having a heart attack is ( 40 % ). It is also assumed that a meditation and yoga course reduce the risk of heart attack by ( 30 % ) and prescription of certain drug reduces its chances by ( 25 % ). At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga? | 12 |

397 | Two digit numbers are formed using the digits 0,1,2,3,4,5 where digits are not repeated. ( P ) is the event that the number so formed is even ( Q ) is the event that the number so formed is greater than 50 ( R ) is the event that the number so formed is divisible by 3 Then write the sample space ( S ) and | 12 |

398 | If ( frac{1-3 p}{2}, frac{(1+4 p)}{3}, frac{1+p}{6} ) are the probabilities of three mutually exclusive and exhaustive events,then the set of all values of p is B. ( left[-frac{1}{4}, frac{1}{3}right] ) c. ( left[0, frac{1}{3}right] ) ( D cdot(0, infty) ) | 12 |

399 | A bag contains cards which are numbered from 2 to ( 90 . ) A card is drawn at random from the bag. Find the probability that it bears (i) a two digit number (ii) a number which is a perfect square | 12 |

400 | Out of 2 men and 3 women a team of two persons is to be formed such that there is exactly one man and one woman. Write the sample space of this experiment, then the total no. of combinations of team possible are A . 9 B. 6 ( c cdot 4 ) D. 12 | 12 |

401 | If ( frac{1+4 p}{4}, frac{1-p}{4}, frac{1-2 p}{4} ) are probabilities of three mutually exclusive and exclusive and exhaustive events, then the possible value of ( p ) belong to the set ( mathbf{A} cdotleft(0, frac{2}{3}right) ) В. ( left[0, frac{1}{2}right] ) ( mathbf{c} cdotleft[-frac{1}{4}, frac{1}{2}right] ) D. ( left[-frac{2}{3}, frac{2}{3}right] ) | 12 |

402 | It is given that event ( A & B ) are such ( operatorname{that} boldsymbol{P}(boldsymbol{A})=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{B}}right)= ) ( frac{1}{2}, Pleft(frac{B}{A}right)=frac{2}{3}, ) then ( P(B)= ) ( A cdot frac{1}{3} ) B. ( frac{2}{3} ) ( c cdot frac{1}{2} ) D. | 12 |

403 | Assertion A fair coin is being tossed four times. Consider the following events: A is the event all four results are the same. B is the event exactly one Head occurs. ( mathrm{C} ) is the event at least two Heads occur | 12 |

404 | There are three different Urns, Urn-I, Urn-II and Urn-III containing 1 Blue, 2 Green, 2 Blue, 1 Green, 3 Blue, 3 Green balls respectively. If two Urns are randomly selected and a ball is drawn from each Urn and if the drawn balls are of different colours then the probability that chosen Urn was Urn-I and Urn-II is A ( cdot frac{1}{7} ) B. ( frac{5}{13} ) c. ( frac{5}{14} ) D. ( frac{5}{7} ) | 12 |

405 | Kamal and Monika appeared for an interview for two vacancies. The probability of Kamal’s selection is ( frac{1}{3} ) and that of Monika’s selection is ( frac{1}{5} . ) Find the probability that at least one of them will be selected. | 12 |

406 | f ( A ) and ( B ) are two events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

407 | Find the value of ( mathrm{K} ) | 12 |

408 | Two symmetrical dice are thrown 200 times. Getting a sum of 9 points is considered to be a success. The probability distribution of successes is ( ^{mathbf{A}} cdotleft(200, frac{1}{9}, frac{8}{9}right) ) в. ( left(200, frac{2}{9}, frac{7}{9}right) ) ( ^{mathrm{c}} cdotleft(200, frac{4}{9}, frac{5}{9}right) ) D ( cdotleft(200, frac{1}{4}, frac{3}{4}right) ) | 12 |

409 | If ( A ) and ( B ) are independent events such ( operatorname{that} boldsymbol{P}(boldsymbol{A})>mathbf{0}, boldsymbol{P}(boldsymbol{B})>mathbf{0}, ) then A. ( A ) and ( B ) are mutually exclusive B. ( A ) and ( bar{B} ) are dependent c. ( bar{A} ) and ( B ) are dependent ( Pleft(frac{A}{B}right)+Pleft(frac{bar{A}}{B}right)=1 ) | 12 |

410 | A family has two children. What is the probability that both the children are boys given that at least one of them is a boy? | 12 |

411 | Thirty-two player ranked 1 to 32 are play knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is ( p ), then the value of ( [2 / p] ) is, where [.] represents the greatest integer function. | 12 |

412 | Each of the urns contains 4 white and 6 blackballs. The ( (n+1) ) th urn contains 5 white and 5black balls. One of the ( (n+1) ) urns is chosen atrandom and two balls are drawn from it withoutreplacement and both the balls turn out to beblack. Then the probability that the ( (n+1) ) th urn was chosen to draw the balls is ( 1 / 16 ) the value of ( n ) is A . 10 в. 11 c. 12 D. 13 | 12 |

413 | For two events ( A ) and ( B, P(A cap B) ) is This question has multiple correct options ( mathbf{A} cdot ) not less than ( P(A)+P(B)-1 ) B. not greater than ( P(A)+P(B) ) C . equal to ( P(A)+P(B)-P(A cup B) ) D・equal to ( P(A)+P(B)+P(A cup B) ) | 12 |

414 | The odds that a book will be reviewed favourably by three independent critics are 5 to 2,4 to 3 and 3 to 4 respectively; what is the probability that of three reviews a majority will be favourable? A ( cdot p=frac{149}{343} ) В. ( p=frac{209}{343} ) c. ( _{p}=frac{129}{3 frac{13}{33}} ) D. ( _{p}=frac{185}{343} ) | 12 |

415 | A die is thrown 200 times and the outcomes 1,2,3,4,5,6 have frequencies as below: Outcome Frequency ( begin{array}{llll}10 & 38 & 43 & 29end{array} ) Find the probabilities of getting a number more than 1 and less than 6 in a toss (trial) A . 0.65 в. 0.55 c. 0.69 D. None of these | 12 |

416 | An urn contains 11 balls numbered from to ( 11 . ) If a ball is selected at random, what is the probabiloity of having a ball with a number which is mutliple of either 2 or ( 3 ? ) A ( cdot frac{7}{11} ) в. ( frac{8}{11} ) c. ( frac{4}{11} ) D. ( frac{6}{11} ) | 12 |

417 | Find probability of bag chosen out random contains more than ( 5 mathrm{kg} ) A . 0.7 B. 0.8 ( c .0 .9 ) D. 0.6 | 12 |

418 | From three men and two women, environment committee of two person to be formed. Condition for event ( boldsymbol{A} ) : There must be at | 12 |

419 | A bag A contains 4 green and 6 red balls. Another bag B contains 3 green and 4 red balls. If one ball is drawn from each bag, find the probability that both are green. ( A cdot 13 / 70 ) B. ( 1 / 4 ) ( c cdot 6 / 35 ) D. 8/35 | 12 |

420 | If ( boldsymbol{P}(boldsymbol{A})=frac{4}{5} ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=frac{2}{5}, ) find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) | 12 |

421 | A person is know to speak the truth 4 times out of ( 5 . ) He throws a die and reports that it is a ace. The probability that it is actually a ace is A. ( 1 / 3 ) в. 2 ( / 9 ) c. ( 4 / 9 ) D. ( 5 / 9 ) | 12 |

422 | 19. A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even no. of trials is (2005S) (a) 5/11 (b) 5/6 (c) 6/11 (d) 1/6 | 12 |

423 | In a single toss of a coin the events ( {mathrm{H}} ) ( {T} ) are mutually exclusive. Write 1 if true and 0 if false | 12 |

424 | A machine has fourteen identical components that function independently. It will stop working if three or more components fail. If the probability that a component fails is equal to ( 0.1, ) find the probability that the machine will be working. | 12 |

425 | ( A ) is a set containing ( n ) elements. subset ( P ) of ( A ) is chosen at random. The set ( A ) is reconstructed by replacing the elements of the subset P.A subset Q of A is again chosen at random. The probability that where ( |boldsymbol{X}|= ) number of elements in ( mathbf{X} ) | 12 |

426 | In a throw of coin, find the probability of getting a head. | 12 |

427 | Abag contains 6 white and an unknown number of black balls ( (leq 3) ) Balls are drawn one by one with replacement from this bag twice and is found to be white on both occasion. Find the probability that the bag had exactly’ ( 3^{prime} ) Black balls. | 12 |

428 | An unbiassed coins are tossed. Find the probability of getting at most one head. | 12 |

429 | Two numbers are selected at random from integers 1 through ( 9 . ) If the sum is even, find the probability that both the numbers are odd. | 12 |

430 | Two aeroplanes I and II bomb a target in succession. The probabilities of I and I scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is A . 0.06 в. ( frac{7}{22} ) ( c .0 .2 ) D. 0.7 | 12 |

431 | A die having six faces is tossed 80 times and the data is as below: outcome [ begin{array}{ccc} 3 & 4 \ & \ & \ & \ 10 & 28 end{array} ] Frequency ( begin{array}{ll}20 & 0 \ 0 & 10 \ 2 & 0end{array} ) Find ( P(1) ) A. 0.175 в. 0.135 ( c cdot 0.145 ) D. 0.125 | 12 |

432 | If ( bar{E} ) and ( overline{boldsymbol{F}} ) are the complementary events of events ( boldsymbol{E} ) and ( boldsymbol{F} ) respectively and if ( mathbf{0}<boldsymbol{P}(boldsymbol{F})<mathbf{1}, ) then: This question has multiple correct options ( mathbf{A} cdot P(E / F)+P(bar{E} / F)=1 ) B cdot ( P(E / F)+P(E / bar{F})=1 ) C ( cdot P(bar{E} / F)+P(E / bar{F})=1 ) D ( cdot P(E / bar{F})+P(bar{E} / bar{F})=1 ) | 12 |

433 | A manufacturing firm produces steel pipes in three planet with daily production daily production of 500 1000 and 2000 units reespectively. According to past experience, it is known that the fraction of defective output produced by the three planets are respectively ( 0.005,0.008,0.010 . ) if ( a ) pipe is selected from a day’s total production and faund to be defective, find the probability that is has come from the first plant | 12 |

434 | ( A ) speak the truth 8 times out of 10 times. A dice is tossed. He reports that it was ( 5 . ) What is the probability that it was actually 5 | 12 |

435 | The probability that a student ( x ) participates in a competition is 0.4 while that for student ( y ) is ( 0.5 . ) The probability that ( x ) participates in competition, given that ( y ) also participates is ( 0.7 . ) Then This question has multiple correct options A. The probability that both ( x ) and ( y ) participates in that competition simultaneously is 0.35 B. The probability that ( y ) participates in that competition given that ( x ) also participates is ( frac{7}{8} ) C. The probability that atleast one of them participates in that competition is 0.55 D. The probability that exactly one of them participates in that competition is 0.20 | 12 |

436 | In a business venture a man can make a profit of Rs. ( 2000 /- ) with probability of 0.4 or have a loss of Rs. ( 1000 /- ) with probability 0.6. His expected profit is A. Rs. ( 800 /- ) B. Rs. ( 600 /- ) c. Rs. ( 200 /- ) D. Rs. 400/- | 12 |

437 | Define event | 12 |

438 | A bag contains 3 red and 2 black balls. One ball is drawn from it at random. Find the probability of drawing a red ball. | 12 |

439 | A game has 2 spinners. Spinner ( # 1 ) has a probability of landing red of ( 2 / 3 . ) And, spinner#2 has a probability of landing red of ( 1 / 5 ) What is the probability spinner#1 lands red AND spinner#2 does NOT land red? A . ( 2 / 15 ) B. ( 8 / 15 ) c. ( 13 / 15 ) D. 1 E. ( 3 / 5 ) | 12 |

440 | An unbiased cubical die whose faces are numbered 1 to 6 is rolled once. Find the probability of getting a square number on the top face. | 12 |

441 | If ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{boldsymbol{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} ) and ( P(bar{A} cap B cap bar{C})=frac{1}{3}, ) then what is ( boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) equal to? A ( cdot frac{1}{12} ) B. ( frac{3}{4} ) c. ( frac{1}{15} ) D. | 12 |

442 | A coin is tossed If it shows a tail we draw a ball from a box which contains 2 red and 3 black balls If it shows head we throw a die Find the sample space for this experiment | 12 |

443 | Bag I contains 1 white, 2 black and 3 red balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white, 3 black and 2 red balls. A bag is chosen at random and two balls are drawn from it with replacement. They happen to be one white and one red. What is the probability that they came from Bag III. | 12 |

444 | Any subset of sample space is called A. event B. probability c. outcome D. exprement | 12 |

445 | If ( P(n o t A)=0.7, P(B)=0.7 ) and ( P(B / A)=0.5, ) find ( P(A bigcup B) ) | 12 |

446 | Define experiment | 12 |

447 | Check whether the probabilities ( boldsymbol{P}(boldsymbol{A}) ) and ( P(B) ) are consistently defined ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= ) ( mathbf{0 . 6} ) | 12 |

448 | It is known that ( 60 % ) mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that none contact the disease. | 12 |

449 | Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. The variance of the number of aces is A ( .24 / 169 ) B . ( sqrt{24 / 169} ) c. ( sqrt{24 / 173} ) D. ( 24 / 173 ) | 12 |

450 | If ( P(A)=frac{7}{13}, P(B)=frac{9}{13} ) and ( P(A cap ) ( B)=frac{4}{13}, ) find ( P(A / B) ) | 12 |

451 | A die is thrown 400 times, the frequency of the outcomes of the events are given as under. outcome ‘ ( mathbf{3} ) 3. ( mathbf{2} ) 4 Frequency 70 65 60 1 75 Find the probability of occurrence of an odd number. A ‘ the probability of occurrence of odd number ( =frac{5}{7} ) B. The probability of occurrence of odd number ( =frac{9}{2} ) C ‘ the probability of occurrence of odd number ( =frac{193}{400} ) D. The probability of occurrence of odd number ( =frac{200}{299} ) | 12 |

452 | Two unbiased coins whose faces are marked 1 and 2 are tossed. The mean value of the total of the numbers is A . 3 B. 4 ( c .5 ) D. | 12 |

453 | Q Type your question ( y ) Development Houses ( 2 mathrm{Br} quad 3 mathrm{Br} quad 4 mathrm{Br} quad ) Total single-Family ( 5 quad 19 quad 34 ) 58 Townhouse ( 24 quad 42 quad 30 ) 96 Total ( 29 quad 61 quad 64 ) A daycare centre is planning to distribute pamphlets to the families with children living houses with three or more bedrooms, due to budget. In addition to sending out flyers, it also decides to send out invitations for a free day of daycare, to the family residing in two categories with the most houses. If a house that already received a flyer is chosen at random to receive the second stage of the marketing, then the probability that the house belongs to one of these two groups is ( frac{p}{q}, ) where ( p, q ) are co-primes.What is the value of ( boldsymbol{q}- ) ( boldsymbol{p} ? ) | 12 |

454 | In the experiment of rolling a dice, find the probability of getting an even number that is multiple of 3. A ( cdot frac{2}{5} ) B. ( frac{2}{3} ) ( c cdot frac{3}{5} ) D. None of these | 12 |

455 | Given two independence events ( A ) and ( B, ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) | 12 |

456 | There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is ( 3 / 10 ) and that of picking up a yellow marble is ( 1 / 2 ) The probability of picking up a black ball is A ( .1 / 5 ) B. 1/10 ( c cdot 1 / 4 ) D. ( 4 / 5 ) | 12 |

457 | An ordinary pack of 52 cards is well shuffled. The top card is then turned over. What is the probability that the top card is a red card. | 12 |

458 | A symmetrical die is thrown four times and getting a multiple of 2 is considered to be a success. The mean and variance of success are A ( cdot 4,2 ) в. 2,1 c. 0,2 D. 1,2 | 12 |

459 | When 2 dice are thrown simultaneously what is the probability that there is exactly one ( 5 ? ) A ( cdot frac{4}{36} ) в. ( frac{5}{18} ) c. ( frac{6}{23} ) D. ( frac{7}{24} ) | 12 |

460 | Given, ( P(A)=frac{3}{5} ) and ( P(B)=frac{1}{5} . ) Find ( P(A text { or } B), ) if ( A ) and ( B ) are mutually exclusive events. | 12 |

461 | Every elementary event associated with a random experiment has probability | 12 |

462 | Suppose we have four boxes ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} ) and ( D ) containing colored marbles as given : One of the boxes has been selected at | 12 |

463 | There are three coins. One is a two- headed coin another is a biased coin that comes up heads ( 75 % ) of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two-headed coin? | 12 |

464 | Out of 48 cricket matches between India and England, India won toss 12 times. How many times England won toss? A . 12 B . 24 ( c .36 ) D. 48 | 12 |

465 | The following is probabilty distribution of r.v X. [ begin{array}{lllllll} mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \ p(x) & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6} end{array} ] then value of k is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) D. 3 | 12 |

466 | Given two independent events ( A ) and ( B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6 .} ) Find ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right) ) | 12 |

467 | Let ( E^{c} ) denote the complement of an event Let ( E, F, G ) be pairwise independent events with ( P(G)>0 ) and ( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F} cap boldsymbol{G})=mathbf{0} operatorname{then} boldsymbol{P}left(boldsymbol{E}^{c} cap boldsymbol{F}^{c} mid boldsymbol{G}right) ) equals ( mathbf{A} cdot Pleft(E^{c}right)+Pleft(F^{c}right) ) B . ( Pleft(E^{c}right)-Pleft(F^{c}right) ) ( mathbf{c} cdot Pleft(E^{c}right)-P(F) ) D. ( P(E)-Pleft(F^{c}right) ) | 12 |

468 | An unbiased die bearing the integers -2 to 3 is thrown once find the probability that the number drawn is, A perfect square | 12 |

469 | Let ( A ) and ( B ) be two events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) geq mathbf{3} / mathbf{4} ) and ( mathbf{1} / mathbf{8} leq boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B}) leq mathbf{3} / mathbf{8} ) Statement 1: ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B}) geq mathbf{7} / mathbf{8} ) statement 2: ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B}) leq 11 / 8 ) A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1 B. Both the statements are TRUE and STATEMENT 2 is not the correct explanation of STATEMENT c. STATEMENT1 is TRUE and STATEMENT 2 is FALSE D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE | 12 |

470 | A bag contains 5 white and 7 black balls; if two balls are drawn what is the chance that one is white and the other black? | 12 |

471 | Suppose a machine produces metal parts that contain some defective parts with probability ( 0.05 . ) How many parts should be produced in order that the probability of atleast one part being defective is ( frac{1}{2} ) or more? (Given that, log ( _{10} 95=1.977 ) and ( left.log _{10} 2=0.3right) ) This question has multiple correct options A . 11 в. 12 ( c cdot 15 ) D. 14 | 12 |

472 | Three coins are tossed together Find, The probability of getting no tail | 12 |

473 | f 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains excatly 3 balls, is: | 12 |

474 | In a simultaneous throw of a pair of dice, if the probability of getting neither 9 nor 11 as the sum of the numbers on the faces is ( frac{5}{a} . ) Find ( a ) | 12 |

475 | A single letter is selected at random from the word’PROBABILITY’. The probability that it is a vowel is: A . ( 3 / 11 ) B. ( 4 / 11 ) c. ( 2 / 11 ) D. | 12 |

476 | The range of a random variable ( boldsymbol{X} ) is {0,1,2} and given that ( P(X=0)= ) ( mathbf{3 c}^{3}, quad boldsymbol{P}(boldsymbol{X}=mathbf{1})=mathbf{4 c}- ) ( mathbf{1 0 c}^{2}, quad boldsymbol{P}(boldsymbol{X}=mathbf{2})=mathbf{5} c-mathbf{1}, ) find (i) the value of ( c ) (ii) ( boldsymbol{P}(boldsymbol{X}<mathbf{1}), quad boldsymbol{P}(1<boldsymbol{X} leq ) 2) ( , quad P(0<X leq 3) ) | 12 |

477 | A bag contains 5 white, 7 red and 3 black balls. If a ball is chosen at random Find the probability that it is not red. | 12 |

478 | In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find how many can speak English only. | 12 |

479 | A die is thrown: ( boldsymbol{P} ) is the event of getting an odd number ( Q ) is the event of getting an even number. ( R ) is the event of getting a prime number. Which of the following pairs is mutually exclusive? A. ( P, Q ) в. ( Q, R ) ( c . P, R ) D. None of these | 12 |

480 | Let ( X ) and ( Y ) be two random variables. The relationship ( boldsymbol{E}(boldsymbol{X} boldsymbol{Y})=boldsymbol{E}(boldsymbol{X}) ) ( boldsymbol{E}(boldsymbol{Y}) ) holds A . Always B. If ( E(X+Y)=E(X)+E(Y) ) is true c. If ( X ) and ( Y ) are independent D. If ( X ) can be obtained from ( Y ) by a linear transformation | 12 |

481 | A family has two children. What is the probability that both the children are boys, given that atleast one of them is a boy? | 12 |

482 | Tell whether the following is certain to happen, possible can happen but not certain. A die when tossed shall land up with 8 on top. | 12 |

483 | The probability of an event A occurring is 0.5 and of B occuring ( s 0.3 . ) If ( A ) and ( B ) are mutually exclusive events, then the probability of neither A nor B occurring is A . 0.6 B. 0.5 ( c .0 .7 ) D. none of these | 12 |

484 | In a school, there are 1000 students, out of which 430 are girls. It is known that out of ( 430,10 % ) of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that chosen student is a girl? | 12 |

485 | A random variable ( boldsymbol{X} ) has the following probability distribution: [ begin{array}{lcccc} begin{array}{l} text { Values } \ text { of } mathbf{X}: end{array} & -2 & -1 & 0 & 1 \ hline P(x): & 0.1 & mathrm{k} & 0.2 & 2 mathrm{k} \ & & & & \ & P(x): & & & end{array} ] Find the value of ( a, ) if ( k=frac{1}{a} ) | 12 |

486 | A discrete random variable X has the probability distribution given below: ( x= ) 1 0.5 1.5 2 ( P(x): ) ( k ) ( 3 k ) ( 2 k ) The Find the value of ( mathrm{k} ) | 12 |

487 | Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 2 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 8} ) ( P(B)=0.25 ) | 12 |

488 | Define random experiment | 12 |

489 | Suppose ( A ) and ( B ) are independent events with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7} ) .Then compute: a) ( P(A cap B) ) b) ( P(A cup B) ) ( mathbf{c}) boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) ) d) ( Pleft(A^{c} cap B^{c}right) ) | 12 |

490 | Cards marked with numbers 4 to 99 are placed in a box and mixed thoughtly. One card is drawn from this box. Find the probability that the number on the card is a perfect square between 91 and ( mathbf{9 9} ) | 12 |

491 | The table gives the probability distribution of a random variable ( boldsymbol{X} ) [ begin{array}{lll} x & 1 & 2 \ P(X= & & end{array} ] ( x) ) 0.2 0.1 [ begin{array}{ll} 0.3 & 0.3 end{array} ] (i) Find ( P ) (ii) Find the mean of ( boldsymbol{X} ) (iii) Find the variance of ( boldsymbol{X} ) | 12 |

492 | Three coins are tossed. Describe two events ( A ) and ( B ) which are mutually exclusive. | 12 |

493 | The probability of student ( A ) passing an examination is ( 2 / 9 ) and of students, ( B ) passing is ( 5 / 9 . ) Assuming the two events: ( A ) passes’. ( B ) passes’ as independent, find the probability of only ( B ) passing the examination | 12 |

494 | Toss a coin for number of times as shown in the table. And record your findings in the table. Number of heads heads | 12 |

495 | Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both balls are red | 12 |

496 | A coin is tossed and a die is thrown simultaneously : ( P ) is the event of getting head and a odd number. ( Q ) is the event of getting either ( H ) or ( T ) and an even number. ( R ) is the event of getting a number on die greater than 7 and a tail. ( S ) is the sample space. Which of the following options is correct? A ( . n(S)=12, n(P)=3, n(Q)=2, n(R)=0 ) В. ( n(S)=12, n(P)=3, n(Q)=3, n(R)=0 ) c. ( n(S)=12, n(P)=3, n(Q)=6, n(R)=0 ) D. ( n(S)=12, n(P)=3, n(Q)=5, n(R)=0 ) | 12 |

497 | If a leap year is selected at random, what is the chance that it will contain 53 tuesdays? | 12 |

498 | In a group of 1000 people, there are 750 people who can speak Hindi and 400 who can speak English. Then number of persons who can speak Hindi only is A . 300 в. 400 c. 600 D. None of these | 12 |

499 | If ( A ) and ( B ) are two events in a sample space ( S ) such that ( P(A) neq 0 ) and ( boldsymbol{P}(boldsymbol{B}) neq boldsymbol{0}, ) then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) A ( cdot P(A) cdot P(B) ) в. ( P(A) . Pleft(frac{B}{A}right) ) ( mathbf{c} cdot P(B) ) D cdot ( P(A) ) | 12 |

500 | Given that she does not achieve success, the chance she studied for 4 hour, is A ( cdot frac{18}{26} ) в. ( frac{19}{26} ) c. ( frac{20}{26} ) D. ( frac{21}{26} ) | 12 |

501 | Verify that the following function can be regarded as p.d.f for the random variable ( boldsymbol{X} ) -1 begin{tabular}{r} 1 \ hline end{tabular} ( mathbf{0} ) 1 ( P(x) ) -0.2 0.2 | 12 |

502 | produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group ( boldsymbol{X} ) consisted of 100 people who observed early bedtimes, and Group ( Y ) consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group ( Y ? ) Dreams Recalled during One Week begin{tabular}{|l|c|c|c|c|} hline & None & 1 to 4 & 5 or more & Total \ hline hline Group X & 15 & 28 & 57 & 100 \ hline Group Y & 21 & 11 & 68 & 100 \ hline Total & 36 & 39 & 125 & 200 \ hline end{tabular} ( A ) ( frac{68}{100} ) B. ( frac{79}{100} ) ( c ) ( frac{79}{164} ) D. ( frac{16}{text { ? }} ) | 12 |

503 | Marks in an aptitude test given to 800 students of a school was found to be normally distributed. 10% of the students scored below 40 Marks and ( 10 % ) of the students scored above 90 marks. Find the number of students who scored between 40 and 90 | 12 |

504 | The probability of an event that cannot happen is ( _{–}-_{-} ? ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) ( D ) | 12 |

505 | Find the probability that a number selected at random from the numbers 3 ( 4,5, dots, 25 ) is prime | 12 |

506 | If ( A ) and ( B ) are independent events of ( a ) random experiment such that ( P(A cap B)=frac{1}{6} ) and ( P(bar{A} cap bar{B})=frac{1}{3} ) then ( boldsymbol{P}(boldsymbol{A})= ) A ( cdot frac{1}{4}, frac{1}{3} ) B. ( frac{1}{2}, frac{1}{3} ) c. ( frac{1}{2}, frac{1}{5} ) D. ( frac{2}{3}, frac{1}{5} ) | 12 |

507 | A number is chosen at random from among the 1 st 50 natural numbers. The probability that the number chosen is either a prime number or a multiple of 5 is A ( cdot frac{12}{25} ) B. ( frac{1}{2} ) c. ( frac{14}{25} ) D. | 12 |

508 | Find the number of ways of permuting the letters of the word PICTURE so that (i) All vowels come together (ii) No two vowels come together (iii) The relative positions of vowels and consonants are not disturbed | 12 |

509 | An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are 2: 1 and the odds in favor of the price remaining the same are ( 1: 3 . ) The probability that the price of the stock will go down during the next week, is A ( cdot frac{4}{12} ) в. ( frac{5}{12} ) ( c cdot frac{7}{12} ) D. none of these | 12 |

510 | Three coins are tossed. Describe two events ( A ) and ( B ) which are mutually exclusive but not exhaustive. | 12 |

511 | A random variable ( X ) has the probability distribution ( X=x: ) ( begin{array}{llllllll}1 & , 2 & , 3 & , 4 & , 5 & , 6 & , 7 & , 8end{array} ) ( boldsymbol{P}(boldsymbol{X}) ) ( mathbf{0 . 1 5}, mathbf{0 . 2 3}, mathbf{0 . 1 2}, mathbf{0 . 1}, mathbf{0 . 2}, mathbf{0 . 0 8}, mathbf{0 . 0 7}, mathbf{0 . 0 5} ) Events ( boldsymbol{E}={mathrm{X} text { is a prime number }} ) and ( boldsymbol{F}=boldsymbol{X} / boldsymbol{X}<mathbf{4} ) ( boldsymbol{i}: boldsymbol{p}(boldsymbol{E} cup boldsymbol{F})=mathbf{0 . 2 3} ) ( boldsymbol{i} boldsymbol{i}: boldsymbol{p}(overline{boldsymbol{E}} cup overline{boldsymbol{F}})=mathbf{0 . 6 5} ) Which of ( I, I I ) is (are) true? A. I only B. II only c. both ( I ) and ( I I ) D. neither I nor ( I I ) | 12 |

512 | If the probabilities of the events ( boldsymbol{A} cap ) ( B, A, B ) and ( A cup B ) are in A.P.with second term of A.P. is equal to common difference then ( A ) and ( B ) are A. independent B. equally likely c. mutually exclusive D. can’t be determined | 12 |

513 | In a school, ( 14 % ) of students take computer classes and ( 67 % ) take drama classes.What is the probability that a student neither takes computer class nor takes drama class? A ( frac{8}{100} ) в. ( frac{29}{100} ) c. ( frac{53}{100} ) D. ( frac{19}{100} ) | 12 |

514 | 22. Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one 31 failure is greater than or equal to then p lies in the interval [2011] | 12 |

515 | An urn contains one black ball and one green ball. A second urn contains one white and one green ball. One ball is drawn at random from each urn.Find the probability of getting at least one green ball. A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{2}{3} ) D. | 12 |

516 | Given two independent events ( A, B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} ) Determine ( boldsymbol{P}(boldsymbol{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{B}) ) | 12 |

517 | The probability that Raju arrives on time at school is 0.72 Write down the probability that he will not arrive on time. | 12 |

518 | Five defective mangoes are accidently mixed with 15 good ones. Four mangoes are drawn at random from this lot. Find the probability distribution of the number of defective mangoes. | 12 |

519 | ( A ) bag ( X ) contains 4 white balls and 2 black balls, while another bag ( boldsymbol{Y} ) contains 3 white balls and 3 black balls Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag ( Y ) | 12 |

520 | Bag A contains 2 red and 3 black balls while another bag ( mathrm{B} ) contains 3 red and 4 black balls. One ball is drawn at random from one of the bag and it is found to be red. Find the probability that it was drawn from bag B. | 12 |

521 | The probability of getting number less than or equal to ( 6, ) when a die is thrown once, is A. An impossible event B. A sure event c. An exhaustive event D. A complementary event | 12 |

522 | The probabilities of three events ( A, B, C ) are events such that ( P(A)= ) ( mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{C})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B})=mathbf{0 . 0 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 2 8}, boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 0 9 .} ) If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}) geq mathbf{0 . 7 5} ) Show that ( P(B cap C) ) lies in the interval [0.23,0.48] | 12 |

523 | A bag contains 4 red and 5 black balls, a second bag contain 3 red and 7 black balls. One ball is drawn at random from each bag, find the probability that the ball are of the same colour. | 12 |

524 | There are 30 tickets numbered from 1 to 30 in a box. A ticket is drawn at random from the box and if ( A ) is the event that the number on the ticket is a multiple of five, write the sample space ( boldsymbol{S}, boldsymbol{n}(boldsymbol{S}) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) ) | 12 |

525 | If coefficients ( a, b, c ) of quadratic equation ( a x^{2}+b x+c=0 ) are chosen at random with replacement from the ( operatorname{set} S=1,2,3,4,5,6, ) find out the probability that roots of quadratic are real and distinct. A ( frac{20}{108} ) в. ( frac{19}{108} ) c. ( frac{21}{108} ) D. ( frac{22}{108} ) | 12 |

526 | A die is thrown 100 times and outcomes are noted as given below: Outcome: 1 3 4 Frequency: ( begin{array}{llll}21 & 9 & 14 & 23end{array} ) If a die is thrown at random, find the probability of getting a/an. 5 | 12 |

527 | 16. Two numbers are selected randomly from the set S={1,2,3 4, 5, 6} without replacement one by one. The probabilité that minimum of the two numbers is less than 4 is (20035 (a) 1/15 (b) 14/15 (c) 1/5 (d) 4/5 | 10 |

528 | A pair of fair coins is tossed yielding the equiprobable space ( mathrm{S}={mathrm{HH}, mathrm{HT}, mathrm{TH}, mathrm{TT}} ) Consider the events: ( A={text { head on first } operatorname{coin}}={mathrm{HH}, mathrm{HT}} ) ( mathrm{B}={text { head on second coin }}={mathrm{HH}, mathrm{TH}} ) ( mathrm{C}={text { head on exactly one coin }}={mathrm{HT}, mathrm{TH}} ) Then check whether ( A, B, C ) are independent or not. | 12 |

529 | For three events ( A, B ) and ( C, P ) (Exactly one of ( boldsymbol{A} text { or } boldsymbol{B} text { occurs })=boldsymbol{P}( ) Exactly one of ( B text { or } C text { occurs })=P(text { Exactly one of } C ) or ( A text { occurs })=frac{1}{4} ) and ( P( ) All the three events occur simultaneously) ( =frac{1}{16} ) Then the probability that at least one of the events occurs, is. A ( cdot frac{7}{32} ) в. ( frac{7}{16} ) c. ( frac{7}{64} ) D. ( frac{3}{16} ) | 12 |

530 | A bag contains 5 white, 7 red and 3 black balls. If a ball is chosen at random, then find the probability that it is not red. | 12 |

531 | One die of red colour one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled its colour and the number on its uppermost face is noted. Describe the sample space | 12 |

532 | The probability of an event ( k ) is A ( .0 geq P(k) geq 1 ) в. ( 0 leq P(k) leq 1 ) c. ( 0>P(k)>1 ) D. ( 0<P(k)<1 ) | 12 |

533 | The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time between 20 and 22 hours? A . 0.3513 B. 0.3216 c. 0.3413 D. 0.3613 | 12 |

534 | A letter is taken out at random from the word ASSISTANT and an other from STATISTICS. The probability that they are the same letters is A ( cdot frac{13}{90} ) в. ( frac{17}{90} ) c. ( frac{19}{90} ) D. ( frac{15}{90} ) | 12 |

535 | If ( mathrm{m} / mathrm{n} ), in lowest terms, be the probability that a randomly chose positive divisor of ( 10^{99} ) is an integral multiple of ( 10^{88} ) than find the value of ( (boldsymbol{m}+boldsymbol{n}) ) | 12 |

536 | A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag. | 12 |

537 | The probability of a sure event (or certain event) is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) ( D ) | 12 |

538 | If 12 persons are seated at a round table, what is the probability that two particular persons sit together? A ( .2 / 11 ) B. 1/11 c. ( 1 / 12 ) D. ( 5 / 12 ) | 12 |

539 | If ( * ) represents 5 balloons then number of symbols to be drawn to represent 60 balloons is ( mathbf{A} cdot mathbf{5} ) B. 60 c. 10 D. 12 | 12 |

540 | A box contain 10 red balls, 20 yellow balls and 50 blue balls. If a ball is drwan at random from the box, find the probability that it will be (i) a blue ball (ii) neither yellow nor blue | 12 |

541 | Form 2 digit number using 0,1,2,3,4,5 without repeating the digits. Write the sample space ( S, ) number of sample points ( n(S), U, n(U) ) for ( U ) is the event that the number so formed is divisible by 5 | 12 |

542 | 19 boys turn out for baseball. Of these 11 are wearing baseball shirts and 14 are wearing baseball pants. There are no boys without one or the other. The number of boys wearing full uniform is ( mathbf{A} cdot mathbf{8} ) B. 6 c. 5 D. 3 | 12 |

543 | A speaks truth in ( 75 % ) of the cases and ( mathrm{B} ) in ( 80 % ) of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact? | 12 |

544 | f ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{B} / boldsymbol{A})= ) 0.6. Find ( P(A / B) ) | 12 |

545 | A baised coin with probability ( boldsymbol{p}(mathbf{0}< ) ( p<1) ) of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is ( frac{2}{5}, ) find ( 3 p ) | 12 |

546 | In a city, three daily newspapers ( A, B, C ) are published. ( 42 % ) of the people in that city read ( A, 51 % ) read ( B ) and ( 69 % ) read ( C .30 ) ( % ) read ( A ) and ( B ; 28 % ) read ( B ) and ( C ; 36 % ) read ( A ) and ( C ; 8 % ) do not read any of the three newspapers. The percentage of persons who read all the three papers is A . ( 25 % ) % B. 18% c. ( 20 % ) D. none of these | 12 |

547 | Three boxes numbered I, II, III contains the balls as follows: ( begin{array}{llll}text { White } & text { Black } & text { Red } \ text { I } & 1 & 2 & 3 \ text { II } & 2 & 1 & 1 \ text { “II } & 4 & 5 & 3end{array} ) One box is randomly selected and a ball is drawn from it. If the ball is red, then find the probability that it is from box II | 12 |

548 | A fair coin is tossed four times and a person win Re 1 for each head and lose Rs. 1.50 for each tail that turns up. Let ( p ) be the probability of person losing Rs 3.50 after 4 tosses.Find ( 4 p ? ) | 12 |

549 | The geometric mean of the observations 2,4,8,16,32,64 is A ( cdot 2^{5 / 2} / 2 ) 2) 1 B ( cdot 2^{7 / 2} ) ( c cdot 33 ) D. None of these | 12 |

550 | Let ( X ) denote the number of hours you study during a randomly selected school day. The probability that ( X ) can take the value ‘x’ has the following from, where ‘k’ is some unknown constant. ( p=(X=X)= ) ( left{begin{array}{ll}mathbf{0 . 1}, & boldsymbol{i f} boldsymbol{x}=mathbf{0} \ boldsymbol{k} boldsymbol{x}, & boldsymbol{x}=mathbf{1} boldsymbol{o r} mathbf{2} \ boldsymbol{k}(mathbf{5}-boldsymbol{x}), & boldsymbol{i f} boldsymbol{x}=mathbf{3} boldsymbol{o r} mathbf{4} \ mathbf{0}, & text { otherwise }end{array}right. ) (a) find the value of ‘k’ (b) what is the probability that you study : (i) at least two hours? (ii) exactly two hours?? (iii) at most 2 hours? | 12 |

551 | The probability that certain electronic component fails when first used is 0.10 If it does not fail immediately, the probability that is lasts for one year is 0.99. The probability that a new component will last for one year is A. 0.891 1 B. 0.692 ( c cdot 0.92 ) D. None of these | 12 |

552 | In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in physics. Then the number of students who have passed in physics only is A . 22 B. 33 c. 10 D. 45 | 12 |

553 | The event which cannot happen is called A . outcome B. impossible event c. frequency D. none of these | 12 |

554 | A fair die is rolled. Consider the events ( boldsymbol{E}={1, mathbf{3}, mathbf{5}} ) and ( boldsymbol{F}={mathbf{2}, mathbf{3}}, ) find ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) ) | 12 |

555 | Suppose an integer from 1 through 100 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9 | 12 |

556 | If ( P(C)=frac{2}{7}, ) then ( P(bar{C})= ) A B. ( frac{2}{7} ) c. 0 D. | 12 |

557 | Define a simple event. | 12 |

558 | Least number of times must a fair die be tossed in order to have a probability of at least ( 91 / 216 ), of getting atleast one six. | 12 |

559 | Find the probability that one will get 75 marks in the question paper of 100 marks. A ( cdot frac{1}{101} ) в. ( frac{75}{100} ) c. ( frac{1}{100} ) D. ( frac{75}{101} ) | 12 |

560 | Lot ( A ) consists of ( 3 G ) and ( 2 D ) articles. Lot ( B ) consists of ( 4 G 1 D ) article. A new lot ( C ) is formed by taking 3 articles from ( A ) articles from ( A ) and 2 form ( B ). The probability that an article chosen at random from ( C ) is A . ( 1 / 3 ) в. 2 / c. ( 8 / 25 ) D. none | 12 |

561 | The average length of time required to complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 35 and 45 minutes to complete the questionnaire? A. About ( 68 % ) B. About ( 72 % ) c. About ( 76 % ) D. About ( 84 % ) | 12 |

562 | A random variable ( X ) has the following probability distribution [ begin{array}{llll} boldsymbol{X}= & -2 & -1 & 0 end{array} ] [ begin{array}{c} P(x) \ text { Then } boldsymbol{E}(boldsymbol{x})= end{array} ] ( begin{array}{llll}0.1 & 0.2 & 0.2end{array} ) A . 0.8 в. 0.9 c. 0.7 D. 1. | 12 |

563 | From a pack of 52 cards, face cards and tens are removed and kept aside, then a card is drawn at random from the remaining cards. If A: The events that the card is drawn is an ace. H: The events that the card is drawn is a heart.S: the events that the card is drawn is a spade. Then, which of the following holds? ( mathbf{A} cdot 9 P(A)=4 P(H) ) B. ( P(S)=4 P(A cap H) ) c. ( 3 P(H)=P(A cap S) ) D. None of these | 12 |

564 | A die is thrown. ( A ) is the event that prime number comes up, ( B ) is the event that the number divisible by three comes up, ( C ) is the event that the perfect square number comes up. Then, ( A, B ) and ( C ) are : A. Mutually exclusive B. Mutually exhaustuve c. Same D. None of these | 12 |

565 | In a certain town, ( 40 % ) of the people have brown hair, ( 25 % ) have brown eyes and 15 ( % ) have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is A . ( 1 / 5 ) B. 3/8 ( c cdot 1 / 3 ) D. ( 2 / 3 ) | 12 |

566 | There are 40 students in a class and their results is presented as below: Result (Pass/Fail) Pass Fail Number of Students 30 If a student chosen at random out of the class, find the probability that the student has passed the examination A . 0.12 B. 0.36 c. 0.65 D. 0.75 | 12 |

567 | There are 30 tickets numbered from 1 to 30 in a box and a ticket is drawn at random. If ( A ) is the event that the number on the ticket is a perfect square, then write the sample ( S, n(S) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) ) | 12 |

568 | A die has 6 faces marked by the given numbers as shown below: The die is thrown once. What is the probability of getting the smallest integer? ( 1 3 longdiv { 2 3 } ) | 12 |

569 | In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in Hindi and Mathematics but not in English? A . 18 в. 12 ( c cdot 10 ) ( D ) | 12 |

570 | Let ( U=R( ) the set of all real numbers ) If ( A={x: x in R, 0<x<2}, B= ) ( {x: x in R, 1<x leq 3} ), then A. ( A cup B={x: x in R text { and } 0<x leq 3} ) B. ( A cap B={x: x in R text { and } 1<x<2} ) c. ( A-B={x: x in R text { and } 0<x leq 1} ) D. all of these | 12 |

571 | If ( A ) and ( B ) are mutually exclusive events, then A ( . P(A)=P(A-B) ) B . ( P(B)=P(A-B) ) c. ( P(A)=P(A cap B) ) D. ( P(B)=P(A cap B) ) | 12 |

572 | A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance? A . 40 B . 45 c. 50 D. 55 | 12 |

573 | A die is thrown. Let ( A ) be the event that the number obtained is greater than 3 Let ( mathrm{B} ) be the event that the number obtained is less than 5. Then ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) is A . 1 B. ( frac{2}{5} ) c. ( frac{3}{5} ) D. | 12 |

574 | In a large metropolitan area, the probabilities are 0.87,0.36,0.36,0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets? | 12 |

575 | A garage mechanic keeps a box of good springs to use as replacements on customers cars. The box contains 5 springs. A colleague, thinking that the springs are for scrap, tosses three faulty springs into the box. The mechanic picks two springs out of the box while servicing a car. Find the probability that the second spring drawn is faulty. A ( cdot frac{1}{8} ) B. ( frac{2}{8} ) ( c cdot frac{3}{8} ) D. ( frac{4}{8} ) | 12 |

576 | Four digit numbers are formed using each of the digits ( 1,2, ldots ldots ., 8 ) only once One number from them is picked at random then the probability that the selected number contains unity is A ( cdot frac{1}{2} ) B. ( frac{1}{8} ) ( c cdot frac{1}{4} ) D. ( frac{1}{3} ) | 12 |

577 | If ( A ) is any event in a sample space then ( Pleft(A^{prime}right) ) is ( A cdot P(A) ) B. ( 1+P(A) ) c. ( 1-P(A) ) D. 1-2P(A) | 12 |

578 | In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is A ( cdot frac{5}{3} ) в. ( frac{3}{5} ) ( c cdot frac{5}{9} ) D. ( frac{9}{5} ) | 12 |

579 | 12. In a school only 3 out of 5 students can participate in a competition What is the probability of the students who do not make it to the competition? 11 | 11 |

580 | There are 6 letters and 3 post-boxes. The number of ways in which these letters can be posted is A ( cdot 6^{3} ) B . ( 3^{6} ) ( mathrm{c} cdot^{6} C_{3} ) D. ( ^{6} P_{3} ) | 12 |

581 | If ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( Pleft(frac{B}{A}right)=0.4 ) then ( Pleft(frac{A}{B}right)=? ) A .0 .32 B. 0.64 c. 0.16 D. 0.25 | 12 |

582 | The experiment is to repeatedly toss a coin until first tail shows up. Identify the type of the sample space. A. Finite sample space B. Continuous sample space c. Infinite discrete sample space D. None of these | 12 |

583 | A prisoner escapes from a jail and is equally likely to choose one of the four roads I, II, III or IV to reach away from the hands of law. If he choose I road, he is successful with probability ( 1 / 6 ) and for I, III and IV this is ( 1 / 8,1 / 10 ) and ( 1 / 12 ). If the prisoner is successful, the probability that he chose road | 12 |

584 | Four persons can hit a target correctly with probabili 1 1 23 and respectively. If all hit at the target indepe dently, then the probability that the target would be hit, JEEM 2019-9 April (M (a) 25 | 12 |

585 | ( boldsymbol{P}(boldsymbol{A})=mathbf{3} / mathbf{8} ; boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{2} ; boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) ( mathbf{5} / mathbf{8}, ) which of the following do/does hold good? This question has multiple correct options A ( cdot Pleft(A^{C} / Bright)=2 Pleft(A / B^{C}right) ) B . ( P(B)=Pleft(A^{C} / Bright) ) C ( cdot 15 Pleft(A^{C} / B^{C}right)=8 Pleft(B / A^{C}right) ) D ( cdot Pleft(A / B^{C}right)=(A cap B) ) | 12 |

586 | Two dice are thrown at a time, find the probability that the sum obtained is less than 6 ( A cdot frac{2}{9} ) B. ( frac{1}{4} ) c. ( frac{5}{18} ) D. ( frac{1}{3} ) | 12 |

587 | 15. If the integers m and n are chosen at random from 1 to 100 then the probability that a number of the form 7m + 7nic divisible by 5 equals (1999 – 2 Marks) (a 1/4 (b) 1/7 (c) 1/8 (d) 1/49 21. a (1 | 11 |

588 | Three coins are tossed. Describe two events ( A ) and ( B ) which are mutually exclusive but not exhaustive. | 12 |

589 | The odds against a certain event are 5 to 2 and the odds in a fvour of another event independent to the former are 6 to 5. Find the probability that none of the events will occur. | 12 |

590 | A, ( mathrm{B} ) are two inaccurate arithmeticians whose chances of solving a given question correctly are ( (1 / 8) ) and ( (1 / 12) ) respectively. They solve a problem and obtained the same result. If it is 1000 to 1 against their making the same mistake, find the chance that the result is correct ( mathbf{A} cdot frac{13}{14} ) B. ( frac{2}{7} ) ( c cdot frac{1}{8} ) D. ( frac{11}{12} ) | 12 |

591 | If ( X ) follows a binomial distribution with parameters ( n=100 ) and ( P=frac{1}{3}, ) then ( P(X=r) ) is maximum when ( r= ) A . 33 B. 50 c. 25 D. none of these | 12 |

592 | ( P ) makes a bet with ( Q ) of 8 pounds to 120 pounds that three races will be won by the three horses ( A, B, C, ) against which the betting is 3 to 2,4 to ( 1, ) and 2 to 1 respectively. The first race having been a on by ( A ), and it being known that the second race was won either by ( B ), or by a horse ( D ) against which the betting was 2 to 1 , find the value of ( P^{prime} s ) expectation. | 12 |

593 | A random variable ( X ) has the following probability distribution: [ begin{array}{cccccc} boldsymbol{X} & mathbf{1} & mathbf{2} & mathbf{3} & mathbf{4} & mathbf{5} \ hline P(X) & k^{2} & 2 k & k & 2 k & 5 end{array} ] [ 5 k^{2} ] Then ( P(X>2) ) is equal to ( mathbf{A} cdot frac{1}{6} ) B. ( frac{7}{12} ) c. ( frac{1}{36} ) D. ( frac{23}{36} ) | 12 |

594 | PTUU 10. Three hous Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is [2005] (d) | 12 |

595 | 17. A die is thrown die is thrown. Let A be the event that the number obtained eater than 3. Let B be the event that the number obtained is less than 5. Then P(AUB) is [2008] (b) 0 (a) 5 (d) 2 | 11 |

596 | In a bolt factory, three machines ( A, B ) and ( C ) manufacture 25,35 and 40 percent of the total bolts respectively. Out of the total bolts manufactured by the machines 5,4 and 2 percent are defective from machine ( A, B & C ) respectively. A bolt is drawn at random and is found to be defective. Find the probability that it was manufactured by (i) Machine A or ( C ) (ii) Machine B. | 12 |

597 | An unbiased die is thrown twice. Let the even ( A ) be ( ^{prime} ) odd ( ^{prime} ) number on the first throw and ( B ) the event ( ^{prime} ) odd number on the second throw’. Check the independence of the events ( A ) and ( B ). | 12 |

598 | An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question? | 12 |

599 | Supposing that it is 9 to 7 against a person A who is now 35 years of age living till he is ( 65, ) and 3 to 2 against a person B now 45 living till he is ( 75 ; ) find the chance that one at least of these persons will be alive 30 years hence. | 12 |

600 | A coin is tossed 100 times with following frequency. Head : 25, Tail : 75 How many outcomes are possible here? A. one B. Two c. three D. Four | 12 |

601 | Let the discrete random variable ( boldsymbol{X}=boldsymbol{x} ) has the probabilities given by ( frac{x}{6} ) for ( x= ) ( 0,1,2,3, ) then its mean is A ( cdot frac{1}{3} ) в. ( frac{5}{3} ) ( c cdot frac{7}{3} ) D. ( frac{9}{3} ) | 12 |

602 | A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red? A ( cdot frac{7}{13} ) в. ( frac{7}{12} ) c. ( frac{8}{13} ) D. ( frac{9}{15} ) | 12 |

603 | Two number are selected at random (without replacement ) from the first six positive integers. Let ( X ) denote the larger of the numbers obtained. Find ( E ) ( (x) ) | 12 |

604 | If ( A ) is an event of a random experiment, then ( A^{C} ) or ( A^{-} ) or ( A^{prime} ) is called the compliment of the event. If true then enter 1 and if false then enter 0 A. 0 B. Can’t determine ( c ) D. None of these | 12 |

605 | If a letter is chosen at random from the English alphabet, if the probability that the letter is a consonant is ( frac{a}{26}, ) then what is the value of ( a ? ) | 12 |

606 | If ( boldsymbol{P}left(boldsymbol{E}_{boldsymbol{k}}right)=boldsymbol{C} ) for ( mathbf{0} leq boldsymbol{k} leq boldsymbol{n}, ) then ( boldsymbol{P}(boldsymbol{A}) ) equals A ( cdot 1 / 2 ) в. ( 2 / 3 ) ( c cdot 1 / 6 ) D. ( 1 /(n+1) ) | 12 |

607 | Une Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is (2007 -3 marks) (a) (b) (c) = T he 1 28. | 12 |

608 | Two coins are tossed simultaneously. Find the probability that either both heads or both tails occur | 12 |

609 | ( A ) and ( B ) are events with ( P(A)= ) ( mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7} ) then compute ( boldsymbol{P}(boldsymbol{A} cap ) ( B) ) | 12 |

610 | If ( A ) and ( B ) are independent events such that ( mathbf{0}<boldsymbol{P}(boldsymbol{A})<mathbf{1}, mathbf{0}<boldsymbol{P}(boldsymbol{B})<mathbf{1}, ) then This question has multiple correct options A. A, B are mutually exclusive B. A and ( bar{B} ) are independent c. ( bar{A} ) and ( bar{B} ) are independent D. ( P(A / B)+P(bar{A} / B)=1 ) | 12 |

611 | A person goes to work by car, train or bus. The probabilities of person travelling by there modes are ( 3 / 10,1 / 2 ) and ( 1 / 5 ) respectively. It is found that chance of person being late for work are ( mathbf{3} / mathbf{7}, mathbf{1} / mathbf{7} ) and ( mathbf{5} / mathbf{7} ) by respective modes Given that on particular day person reaches late, find the probability that on that day he had travelled by train | 12 |

612 | A card is thrown from a pack of 52 cards so that each cards equally likely to be selected. In which of the following cases are the events ( A ) and ( B ) independent? ( A= ) the card drawn is spade, ( B= ) the card drawn in an ace. | 12 |

613 | A box contains 6 red marbles numbers from 1 through 6 and 4 white marbles 12 through 15. Find the probability that a marble drawn ‘at random’ is white and odd numbered A . 5 B. ( frac{1}{5} ) ( c cdot 6 ) D. | 12 |

614 | A card is drawn at a random from a pack of 52 cards. What is the probability of drawing a king or a jack? A . ( 1 / 52 ) в. 2/26 ( c cdot 1 / 13 ) D. 2/13 | 12 |

615 | A die is rolled so that the probability of face ( i ) is proportional to ( i,{i= ) ( 1,2, dots .6} . ) The probability of an even number occurring when the die is rolled is ( A cdot frac{7}{4} ) B. ( frac{4}{7} ) ( c cdot frac{5}{7} ) D. None of these | 12 |

616 | Which one can represent a probability of an event A ( cdot frac{7}{4} ) B. – 1 c. ( -frac{2}{3} ) D. ( frac{2}{3} ) | 12 |

617 | A dice is thrown ( 2 n+1 ) times, ( n epsilon N ) The probability that faces with even numbers show odd number of times is A ( cdot frac{2 n+1}{4 n+3} ) B. less than ( frac{1}{2} ) c. greater than ( frac{1}{2} ) D. none of these | 12 |

618 | Three numbers are chosen at random without replacement from ( 1,2,3, dots . ., 10 ) The probability that the minimum of the chosen numbers is 3 or their maximum is 7 is A ( cdot 1 / 2 ) в. ( 1 / 3 ) c. ( 1 / 4 ) D. ( 11 / 40 ) | 12 |

619 | ( X ) follows a binomial distribution with parameters ( boldsymbol{n}=boldsymbol{6} ) and ( boldsymbol{P} . ) If ( boldsymbol{4} boldsymbol{P}(boldsymbol{x}= ) ( mathbf{4})=boldsymbol{P}(boldsymbol{x}=mathbf{2}), ) then ( boldsymbol{P}= ) A ( cdot frac{1}{2} ) в. ( c cdot frac{1}{6} ) D. | 12 |

620 | A die is rolled, find the probability that an odd numbers is obtained. A ( cdot frac{1}{2} ) B. ( frac{3}{2} ) ( c cdot frac{7}{2} ) D. ( frac{6}{3} ) | 12 |

621 | The sample space in the set representing an event more than one element is called A. compound B. simple c. impossible D. complementary | 12 |

622 | An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is along with another ball of same colour. The process is repeated. the probability that the third ball drawn is black is a/b (no common divisor), then ( b-a= ) | 12 |

623 | A person drawn a card from a pack of 52 cards, replaces it ( & ) shuffles the pack. He continues doing this till the draws a spade. The probability that he will fail exactly the first two times is A ( cdot frac{1}{64} ) в. ( frac{9}{64} ) c. ( frac{36}{64} ) D. ( frac{60}{64} ) | 12 |

624 | A symmetric die is thrown ( (2 n+1) ) times. The probability of getting a prime score on the upturned face at most ( n ) times is A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{4} ) D. | 12 |

625 | The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is ( 0.25 . ) The probability of selecting a white marble at random from the same jar is ( frac{1}{3} . ) If this jar contains 10 yellow marbles. What is the total number of marbles in the jar? | 12 |

626 | If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is (1998 – 2 Marks) (a) 13/32 (b) 1/4 (c) 1/32 (d) 3/16 | 12 |

627 | If ( A ) and ( B ) are two events such that ( P(A cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq frac{3}{8} ) then This question has multiple correct options ( ^{mathbf{A}} cdot P(A)+P(B) leq frac{11}{8} ) в. ( P(A) . P(B) leq frac{3}{8} ) c. ( P(A)+P(B) geq frac{7}{8} ) D. none of these | 12 |

628 | Two aeroplanes ( I ) and ( I I ) bomb a target in succession. The probability of ( boldsymbol{I} ) and ( I I ) scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is A . 0.06 B. 0.14 c. 0.32 D. 0.7 | 12 |

629 | Two events ( A ) and ( B ) will be independent if ( mathbf{A} cdot Pleft(A^{prime} cap B^{prime}right)=(1-P(A))(1-P(B)) ) B ( cdot P(A)+P(B)=1 ) ( mathbf{c} cdot P(A)=P(B) ) D. ( A ) and ( B ) are mutually exclusive | 12 |

630 | A bag contain 4 white, 7 black and 5 red balls. A ball is drawn Find the probability that the ball drawn is red. | 12 |

631 | A problem in mathematics is given to 4 students whose chances of solving individually are ( frac{1}{2}, frac{1}{3}, frac{1}{4} ) and ( frac{1}{5} . ) The probability that the problem will be solved at least by one student is? A ( cdot frac{2}{3} ) в. ( frac{3}{5} ) ( c cdot frac{4}{5} ) D. ( frac{3}{4} ) | 12 |

632 | In a series of 3 one-day cricket matches between teams ( A ) and ( B ) of a college, the probability of team A winning or drawing are ( 1 / 3 ) and ( 1 / 6 ) respectively. If a win, loss or draw gives 2,0 and 1 point respectively, then what is the probability that team A will score 5 points in the series? A ( cdot frac{17}{18} ) B. ( frac{11}{12} ) ( c cdot frac{1}{12} ) D. ( frac{1}{18} ) | 12 |

633 | If ( A ) and ( B ) are two events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{4}, boldsymbol{P}(boldsymbol{B})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= ) ( frac{1}{8} ) find ( P A cup B ) | 12 |

634 | Find the mean of the binomial distribution ( Bleft(4, frac{1}{3}right) ) | 12 |

635 | Jiah is doing an experiment in her math class. She flips four coins in the air. What is most likely to happen? A. Two of the coins will be heads and two will be tails B. Three of the coins will be heads and one will be tail c. All four coins will be heads D. None of the coins will be heads | 12 |

636 | If ( A ) and ( B ) are two events such that ( P(A cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq ) ( mathbf{3} ) ( overline{mathbf{8}}^{prime} ) then This question has multiple correct options A ( cdot P(A)+P(B) geq frac{7}{8} ) B . ( P(A)+P(B) leq 11 / 8 ) ( c cdot P(A) P(B) leq frac{3}{8} ) D. None of these | 12 |

637 | Which of the following experiments does NOT have equally likely outcomes? A. Choose a number at random from 1 to 7 B. Toss a coin c. choose a letter at random from the word school D. None of the above | 12 |

638 | State true or false: The probabilities of three mutually exclusive events ( A, B, C ) are ( P(A)= ) ( frac{2}{3}, P(B)=frac{1}{4}, P(C)=frac{1}{6} ) A. True B. False | 12 |

639 | Events ( E_{1}, E_{2}, E_{3} ) are possible events of an experiment and their probabilities are recorded.Mark the possible correct answers. This question has multiple correct options ( begin{array}{ll}text { A } cdot Pleft(E_{1}right)=0.3, & Pleft(E_{2}right)=0.4, quad Pleft(E_{3}right)=0.3end{array} ) B – ( Pleft(E_{1}right)=0.1, quad Pleft(E_{2}right)=0.4, quad Pleft(E_{3}right)=0.5 ) C ( cdot Pleft(E_{1}right)=0.6, quad Pleft(E_{2}right)=-0.3, quad Pleft(E_{3}right)=0.7 ) D ( cdot Pleft(E_{1}right)=0.4, quad Pleft(E_{2}right)=0.2, quad Pleft(E_{3}right)=0.3 ) | 12 |

640 | post a letter to my friend and do not receive a reply. It is known that one letter out of ( m ) letters do not reach its destination. If it is certain that my friend will reply if he receives the letter If ( A ) denotes the event that my friend receives the letter and ( B ) that I get a reply, then This question has multiple correct options A ( cdot P(B)=(1-1 / m)^{2} ) B . ( P(A cap B)=(1-1 / m)^{2} ) c. ( Pleft(A mid B^{prime}right)=(m-1) /(2 m-1) ) D. ( P(A cup B)=(m-1) / m ) | 12 |

641 | f ( A, B, C ) are three events show that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})+ ) ( boldsymbol{P}(boldsymbol{C})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})-boldsymbol{P}(boldsymbol{b} cap boldsymbol{C})- ) ( boldsymbol{P}(boldsymbol{C} cap boldsymbol{A})+boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}) ) | 12 |

642 | Three numbers are chosen at random without replacement from ( {1,2, ldots, 8 .} ) The probability that their minimum is 3 given that their maximum is 6 is A ( cdot frac{2}{5} ) B. ( frac{3}{8} ) ( c cdot frac{1}{5} ) D. | 12 |

643 | In a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is ( frac{1}{3} ) and the probability that he copies the answer is ( frac{1}{6} . ) The probability that his answer is correct given that he copied it, is ( frac{1}{8} . ) Find the probability that he knew the answer to the question given that he correctly answered it. A ( cdot frac{11}{29} ) B. ( frac{18}{29} ) c. ( frac{15}{29} ) D. ( frac{24}{29} ) | 12 |

644 | Cards marked with number 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number of the card is an even number | 12 |

645 | Two integers are selected at random from the set ( 1,2, ldots, 11 . ) Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is: A ( cdot frac{2}{5} ) B. ( frac{1}{2} ) ( c cdot frac{3}{5} ) D. ( frac{7}{10} ) | 12 |

646 | A biased coin with probability ( P,(0<p< ) 1) of heads is tossed until a head appear for the first time. If the probability that the number of tosses required is even is ( frac{2}{5} ) then ( P= ) ( A cdot frac{2}{5} ) B. ( c cdot frac{2}{3} ) ( D cdot frac{1}{3} ) | 12 |

647 | [ begin{array}{lllll} X=x & -2 & -1 & 0 & 1 \ P(X= & 0.1 & K & 0.2 & 2 K end{array} ] ( x) ) is the probability distribution of random variable ( X ). Find the value of ( K ) and variance of ( boldsymbol{X} ) | 12 |

648 | A market research group conducted a survey of 2,000 consumers and reported that 1720 consumers liked product ( P_{1} ) and 1,4500 consumers liked product ( P_{2} . ) What is the least number that must have liked both the products. | 12 |

649 | There are ( m ) persons sitting in a row. two of them are selected at random. The probability that the two selected persons are not together is ( 1-frac{2}{m} . ) If true enter 1 else 0 | 12 |

650 | 3 cards are given, one of them is red on both sides, one is blue on both sides ( & ) one is blue on one side red on the other side. One of them is chosen randomly ( & ) put on the table. It shows red colour on the upper side. The chance of the other side of the card being red is: | 12 |

651 | The probability that a leap year will have only 52 Sundays is A ( cdot frac{4}{7} ) B. ( frac{5}{7} ) ( c cdot frac{6}{7} ) D. | 12 |

652 | Assertion If ( boldsymbol{B} subset boldsymbol{A}, ) then ( boldsymbol{P}(boldsymbol{A} cap overline{boldsymbol{B}})=boldsymbol{P}(boldsymbol{A})- ) ( boldsymbol{P}(boldsymbol{B}) ) Reason ( (boldsymbol{A} cap overline{boldsymbol{B}}) cup boldsymbol{B}=boldsymbol{A} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

653 | In a box containing only purple and green marshmallows, 6 marshmallows are purple. If the probability of choosing a purple marshmallow from the box is ( frac{1}{3}, ) calculate the number of green marshmallows in the box. ( A cdot 2 ) B. 6 c. 9 D. 12 E . 18 | 12 |

654 | ( X ) and ( Y ) are independent binomial ( operatorname{variates} boldsymbol{A}left(mathbf{5}, frac{mathbf{1}}{mathbf{2}}right) ) and ( boldsymbol{B}left(mathbf{7}, frac{mathbf{1}}{mathbf{2}}right) ) then ( boldsymbol{P}(boldsymbol{X}+boldsymbol{Y}=boldsymbol{3}) ) A ( cdot frac{45}{1024} ) в. ( frac{55}{1024} ) c. ( frac{65}{1024} ) D. ( frac{60}{1024} ) | 12 |

655 | For any two events ( A ) and ( B ) in a sample space This question has multiple correct options ( ^{mathbf{A}} cdot p(A / B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true B . ( P(A cap B)=P(A)-P(bar{A} cap bar{B}) ) does not hold C ( . P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( mathrm{A} ) and ( mathrm{B} ) are independent D. ( P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( mathrm{A} ) and ( mathrm{B} ) are disjoint | 12 |

656 | Sum of the probabilities of all the elementary events of an experiment is ( mathbf{A} cdot mathbf{0} ) B. 0.2 c. 1 D. 0.8 | 12 |

657 | ( boldsymbol{8} boldsymbol{p}(overline{boldsymbol{A}} cap boldsymbol{B}) ) | 12 |

658 | If the sum of the mean and variance of a binomial distribution for 6 trials be ( 10 / 3, ) find the distribution. | 12 |

659 | The probability of an even happens in one trial of an experiment is ( 0.3 . ) Three independent trials of the experiments are performed. Find the probability that the event A happens at least once. A .0 .657 B. 0.965 c. 0.796 D. 0.509 | 12 |

660 | Weight ( 50-quad 56 ) (in ( mathrm{kg}) ) Number of 15 students Garima collected the data regarding weights of students of her class and prepared the above table: A student is to be selected randomly from her class for some competition. The probability of selection of the student is the highest whose weight (in kg) is in the interval A. ( 44-49 ) B. ( 56-61 ) c. ( 50-55 ) D. ( 62-67 ) | 12 |

661 | A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin? A ( cdot frac{41}{70} ) B. ( frac{31}{70} ) c. ( frac{27}{70} ) D. | 12 |

662 | From a well shuffled pack of 52 playing cards, four are drawn at random. The probability that all are spades, but one is a king is: ( ^{mathrm{A}} cdot frac{39}{^{52} C_{4}} C_{4} ) в. ( frac{12}{52} C_{3} ) ( ^{mathrm{C}}-frac{^{39} C_{4}}{^{52} C_{4}} ) D. ( frac{12}{52} C_{4} ) | 12 |

663 | A letter is known to have come from either ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or CALCUTTA. On the envelope just two consecutive letters ( boldsymbol{T} boldsymbol{A} ) are visible. The probability that the letter has come from ( C ) ALCUTTA is A ( cdot frac{4}{11} ) B. ( frac{1}{3} ) c. ( frac{5}{11} ) D. ( frac{4}{7} ) | 12 |

664 | Show that ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cap boldsymbol{B} ) implies ( boldsymbol{A}= ) ( boldsymbol{B} ) | 12 |

665 | In a batch of 10 articles, 4 articles are defective. 6 articles are taken from the batch for inspection If more than 2 articles in this batch are defective, the whole batch is rejected Find the probability that the batch will be rejected. | 12 |

666 | ( mathbf{A} ) & B are sharp shooters whose probabilities of hitting a target are ( frac{mathbf{9}}{mathbf{1 0}} ) ( & frac{14}{15} ) respectively. If it is knownthat exactly one of them has hit the target, then the probability that it was hit by ( A ) is equal to A ( cdot frac{24}{55} ) в. ( frac{27}{55} ) c. ( frac{9}{23} ) D. ( frac{10}{23} ) | 12 |

667 | Which one of the following is an impossible event? This question has multiple correct options | 12 |

668 | Define sure event. | 12 |

669 | Which experiment has equally likely outcomes? A. Choose a number at random from 1 to 7 B. Toss a coin c. Roll a die D. All the above | 12 |

670 | The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3: 2 . It is known that an average of one truck in thirty trucks and two cars in fifty cars stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car ( A cdot frac{4}{9} ) в. ( frac{9}{250} ) ( c cdot frac{3}{5} ) D. ( frac{1}{30} ) | 12 |

671 | A bag contain 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that all the three balls are blue balls A ( cdot frac{7}{93} ) в. ( frac{6}{92} ) c. ( frac{7}{95} ) D. ( frac{8}{95} ) | 12 |

672 | 4 normal distinguishable dice are rolled once. The number of possible outcomes in which at least one dice shows up 2? A . 216 B. 648 c. 625 D. 67 | 12 |

673 | Two unbiased dice are thrown together at random. Find the expected value of the total number of points shown up. | 12 |

674 | There are 4 balls of different colours ( & 4 ) boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is: A . 9 B . 30 c. 20 D. None | 12 |

675 | Two different dice are tossed together Find the probability: (i) of getting a doublet (ii) of getting a sum 10 , of the number on the two dice. | 12 |

676 | Which of the following is an random experiment? This question has multiple correct options A. Rolling a pair of dice B. Choosing 2 marbles from a jar C. Choosing a number at random from 1 to 10 D. Tossing two coins | 12 |

677 | 10. A coin is tossed 200 times and head appeared 120 times The probability of getting a head in this experiment is | 11 |

678 | The probability that a man will live 10 more years, is ( frac{1}{4} ) and the probability that his wife will live 10 more years, is ( mathbf{1} ) – Then, what is the probability that ( overline{mathbf{3}} ) neither will be alive in 10 years? A ( cdot frac{1}{2} ) в. ( frac{3}{7} ) ( c cdot frac{2}{3} ) D. | 12 |

679 | A survey of people in a given region showed that ( 20 % ) were smokers. The probability of death due to lung cancer, given that a person smoked, was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is ( 0.006, ) what is the probability of death due to lung cancer given that a person is a smoker? A ( cdot 1 / 140 ) в. ( 1 / 70 ) ( c cdot 3 / 140 ) D. ( 1 / 10 ) | 12 |

680 | If a random variable ( X ) takes value 0 and 1 with respective probabilities ( frac{2}{3} ) and ( frac{1}{3} ) then the expected value of ( X ) is A ( cdot frac{2}{3} ) B. ( frac{1}{3} ) c. 0 D. | 12 |

681 | If ( frac{2}{11} ) is the probability of an event. What is the probability of the event ‘not ( boldsymbol{A}^{prime} ) | 12 |

682 | A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8 , given that the red die resulted in a number less than 4 | 12 |

683 | A die is thrown 4 times. The probability of getting atmost two 6 is ( mathbf{A} cdot 0.984 ) B. 0.802 c. 0.621 D. 0.72 | 12 |

684 | If a selected student has been found to pass the examination then find out the probability that he is the only student to have passed the examination. ( ^{mathbf{A}} cdot_{Pleft(E_{1} / Aright)}=frac{4}{[n(2 n+1)]^{2}} ) в. ( quad Pleft(E_{1} / Aright)=frac{2}{[n(2 n+1)]^{2}} ) ( ^{mathrm{c}} Pleft(E_{1} / Aright)=frac{4}{[n(n+1)]^{2}} ) D. ( quad Pleft(E_{1} / Aright)=frac{2}{[n(n+1)]^{2}} ) | 12 |

685 | Two dice each numbered from 1 to 6 are thrown together. Let ( A ) and ( B ) be two events given by ( A: ) even number on the first die ( B: ) number on the second die is greater than 4 Find the value of ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) A ( cdot frac{1}{2} ) B. ( frac{1}{4} ) ( c cdot frac{2}{3} ) D. ( frac{1}{6} ) | 12 |

686 | A die is thrown thrice. Find the probability of getting an odd number number at least once. | 12 |

687 | Two symmetrical dice are thrown. The probability of getting a sum of 6 points is A ( cdot frac{4}{36} ) в. ( frac{5}{36} ) c. ( frac{6}{36} ) D. ( frac{1}{36} ) | 12 |

688 | There are three events ( A, B, C ) one which must and only one can happen; the odds are 8 to 3 against ( A, 5 ) to 2 against ( B . ) The odds against ( C ) is 43: 17k. Find the value of ( k ) ? | 12 |

689 | The probability distribution function of a random variable ( boldsymbol{X} ) is given by ( boldsymbol{x}_{i}: quad 0 quad 1 quad 2 ) ( c / 2 quad c quad 2 c ) where ( c>0 . ) Find ( c ) | 12 |

690 | When a dice is thrown, find the probability that either an odd number or a multiple of 4 occurs | 12 |

691 | Which of the following is not true regarding the normal distribution? A. the point of inflecting are at ( X=mu pm sigma ) B. skewness is zero c. maximum heigth of the curve is ( frac{1}{sqrt{2 pi}} ) D. mean = media = mode | 12 |

692 | If ( A ) and ( B ) are two events then This question has multiple correct options ( mathbf{A} cdot P(A cap B) geq P(A)+P(B)-1 ) B ( . P(A cap B) geq P(A)+P(B) ) ( mathbf{c} cdot P(A cap B)=P(A)+P(B)-P(A cup B) ) ( mathbf{D} cdot P(A cap B)=P(A) cdot P(B) ) | 12 |

693 | f ( P(A)=0.40, P(B)=0.35 ) and ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 5 5}, ) then ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})= ) ( A ) 5 B. ( frac{8}{11} ) ( c cdot frac{4}{7} ) D. | 12 |

694 | An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution | 12 |

695 | Two similar boxes ( B_{i}(i=1,2) ) contains ( (i+1) ) red and ( (5-i-1) ) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours? A ( cdot frac{1}{2} ) B. ( frac{3}{10} ) ( c cdot frac{2}{5} ) D. | 12 |

696 | The probability of a man hitting a target in one trial is ( frac{1}{4} . ) The chances of hitting the target at least once in ( n ) trials exceeds ( frac{2}{3}, ) then the value of ( n ) equals ( A cdot 2 ) B. 4 ( c cdot 6 ) D. 8 | 12 |

697 | A random variable ( boldsymbol{X} ) has the following probability distribution: [ begin{array}{ccccc} boldsymbol{X} & 0 & 1 & 2 & 3 \ P(X) & 0.1 & k & 2 k & 2 k end{array} ] Determine: (i) ( k ) (ii) ( P(X geq 2) ) | 12 |

698 | The incidence of occupational disease in an industry is such that the workers have a ( 20 % ) chance of suffering from it. The probability that out of 6 workers chosen at random, not even one will suffer from that disease is ( mathbf{A} cdotleft(frac{1}{5}right)^{6} ) B. ( left(frac{4}{5}right)^{6} ) ( ^{mathbf{c}} cdot_{1}^{6} Cleft(frac{1}{5}right)^{5}left(frac{4}{5}right)^{1} ) ( ^{mathrm{D} cdot}_{1}^{6} Cleft(frac{1}{5}right)^{1}left(frac{4}{5}right)^{5} ) | 12 |

699 | 10 different pens and two different books are distributed randomly to 3 students giving 4 things to each. The probability that books go to different students is A ( cdot frac{5}{11} ) в. ( frac{6}{11} ) ( c cdot frac{7}{11} ) D. ( frac{8}{11} ) | 12 |

700 | 4 bad apples accidentally got mixed up with 20 good apples. In a draw of 2 apples at random, expected number of bad apples is A . 1 в. ( 2 / 3 ) c. ( 1 / 3 ) D. ( 1 / 6 ) | 12 |

701 | If 3 numbers are selected from the first 15 natural numbers, then the probability that the numbers are in A.P is A ( cdot frac{7}{65} ) в. ( frac{9}{65} ) ( c cdot frac{8}{65} ) D. ( frac{6}{65} ) | 12 |

702 | Which one of the following cannot be the probability of an event A ( cdot frac{2}{3} ) в. -1.5 c. ( 15 % ) D. 0.7 | 12 |

703 | A box has tokens numbered 3 to 100 . If a token is taken out at random the chance that the number is divisible by 7 is A ( cdot 1 / 4 ) B. 1/5 ( c cdot 1 / 6 ) D. 1/ | 12 |

704 | Given ( boldsymbol{X}-boldsymbol{B}(boldsymbol{n}, boldsymbol{p}) ) If ( n=10 ) and ( p=0.4, ) find ( E(X) ) and ( operatorname{Var}(boldsymbol{X}) ) | 12 |

705 | Check whether the probabilities ( boldsymbol{P}(boldsymbol{A}) ) and ( P(B) ) are consistently defined ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) ( mathbf{0 . 8} ) | 12 |

706 | Toss three fair coins simultaneously and record the outcomes. Find the probability of getting atmost one head in the three tosses. A ( cdot frac{1}{6} ) B. ( frac{1}{4} ) ( c cdot frac{1}{2} ) D. | 12 |

707 | If ( mathrm{M} ) and ( mathrm{N} ) are any two events, the probability that not exactly one of them occurs is for an event set ( A ), the complement is ( boldsymbol{A}^{o} ) A. ( P(M)+P(N)-2 P(M cap N) ) В. ( P(M)+P(N)-P(M cap N) ) C ( cdot Pleft(M^{o}right)+Pleft(N^{o}right)-2 Pleft(M^{o} cup N^{o}right) ) D. ( Pleft(M cap N^{o}right)+Pleft(M^{o} cup Nright) ) | 12 |

708 | 1 20. Let X and Y be two events such that P(X) = (JEE Adv. 2017 and P (Y|X)= -. Then (a) PCY)= e) P(KoY)= (6) P(X”Y)= (a) P(XUY) = | 12 |

709 | Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) ) | 12 |

710 | From a lot of 10 bulbs, which includes 3 detectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs. | 12 |

711 | 18. Let X and Y be two events such that P(XY)-1 P(Y/X)= ? and P(XnY)= 1. Which of the following is 2. Which of the following is (are) correct ? (2012) (a) P(XUY)= (b) X and Y are independent (C) X and Y are not independent (a) P(xºny) = | 12 |

712 | If ( mathbf{A} ) and ( mathbf{B} ) are two events such that ( P(mathbf{A} cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq frac{3}{8} ) then This question has multiple correct options A ( cdot mathrm{P}(mathrm{A})+mathrm{P}(mathrm{B}) leq frac{11}{8} ) в. c. ( mathrm{P}(mathrm{A})+mathrm{P}(mathrm{B}) geq frac{7}{8} ) D. ( mathrm{P}(mathrm{A}) cdot mathrm{P}(mathrm{B}) geq frac{1}{8} ) | 12 |

713 | Urn ( A ) contains 6 red and 4 black balls and urn ( B ) contains 4 red and 6 black balls. One ball is drawn at random from urn ( A ) and placed in urn ( B ). Then one bal is drawn at random from urn ( B ) and placed in urn ( A ). If one ball is now drawn at random from urn ( A ), the probability that it is found to be red is ( 4 k / 55 . ) Find the value of ( k ) | 12 |

714 | If the probability of defective bolts is 0.1 the sum of the mean and standard deviation for the distribution of defective volts in a total of 500 bolts is ( (a+sqrt{b}), ) then the value of ( a+b ) is | 12 |

715 | If ( A ) and ( B ) are two events, the probability that exactly one of them occurs is given by This question has multiple correct options A. ( P(A)+P(B)-2 P(A cap B) ) В ( cdot Pleft(A cap B^{prime}right)+Pleft(A^{prime} cap Bright) ) c. ( P(A cap B)-P(A cap B) ) D. ( Pleft(A^{prime}right)+Pleft(B^{prime}right)-2 Pleft(A^{prime} cap B^{prime}right) ) | 12 |

716 | If ( A ) and ( B ) are events of the same experiments with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})= ) 0.5, then find the maximum value of ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) | 12 |

717 | A fair die is rolled once. STATEMENT – 1: The probability of getting a composite number is ( 1 / 3 ) STATEMENT – 2: There are three possibilities for the obtained number ( (i) ) the number is a prime number (ii) the number is a composite number (iii) the number is ( 1, ) and hence probability of getting a prime number ( =1 / 3 ) A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement – 1 B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement – c. Statement – 1 is True, Statement – 2 is False D. Statement – 1 is False, Statement – 2 is True | 12 |

718 | There are 6 articles in a box. Write the total numbers of article in 10 such boxes. | 12 |

719 | A fair die is thrown 3 times. The chance that sum of three numbers appearing on the die is less than 11 , is equal to – A ( cdot frac{1}{2} ) B. ( frac{2}{3} ) ( c cdot frac{1}{6} ) D. ( frac{5}{8} ) | 12 |

720 | If ( P(n) ) is the statement ( ” n(n+1) ) is even”, then what is ( boldsymbol{P}(boldsymbol{4}) ) ? | 12 |

721 | For two events ( A ) and ( B ), if ( P(A)= ) ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})=mathbf{1} / mathbf{4} ) and ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A})=mathbf{1} / 2, ) then This question has multiple correct options A. A and B are independent B. A and B are mutually exclusive c. ( Pleft(A^{prime} mid Bright)=3 / 4 ) D. ( Pleft(B^{prime} mid A^{prime}right)=1 / 2 ) | 12 |

722 | Eight players ( boldsymbol{P}_{1}, boldsymbol{P}_{2}, ldots ldots boldsymbol{P}_{8} ) play a knock-out tournament. It is known that whenever the players ( P_{i} ) and ( P_{j} ) play, the player ( boldsymbol{P}_{i} ) will win if ( i<j ). Assuming that the players are paired at random in each round, the probability that the player ( boldsymbol{P}_{4} ) reaches the final is ( boldsymbol{k} / mathbf{7} ) 0. Find ( boldsymbol{k} ) | 12 |

723 | Mother, father and son line up at random for a family photo. If ( A ) and ( B ) are two events given by ( A= ) Son on one end, ( B= ) Father in the middle, find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) ) | 12 |

724 | Let ( A ) and ( B ) be events such that ( boldsymbol{P}(overline{boldsymbol{A}})=frac{4}{5}, boldsymbol{P}(boldsymbol{B})=frac{1}{3}, boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{B}}right)=frac{1}{6} ) then: A ( . P(A cap B) ) в. ( P(A cup B) ) ( ^{mathrm{c}} cdot_{P}left(frac{B}{A}right) ) D. Are ( A ) and ( B ) independent | 12 |

725 | One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king? A ( cdot frac{1}{2} ) в. ( frac{6}{13} ) c. ( frac{7}{13} ) D. ( frac{27}{52} ) | 12 |

726 | For two independent events ( A ) and ( B ) what is ( P(A+B), operatorname{given} P(A)=frac{3}{5} ) and ( P(B)=frac{2}{3} ? ) A ( cdot frac{11}{15} ) в. ( frac{13}{15} ) ( c cdot frac{7}{15} ) D. 0.65 | 12 |

727 | 13. At a telephe a telephone enquiry system the number of phone cells arding relevant enquiry follow Poisson distribution with age of 5 phone calls during 10 minute time intervals be probability that there is at the most one phone call during a 10-minute time period is (2006) (a) (b) | 12 |

728 | Three coins are tossed. Find the probability of getting atleast two head. | 12 |

729 | A bag contains 10 white and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black? | 12 |

730 | A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that all of them are in wrong envelope. | 12 |

731 | For any two events ( A ) and ( B ) in a sample space: This question has multiple correct options ( ^{mathbf{A}} cdot p(A mid B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true B ( . P(A cap bar{B})=P(A)-P(A cap B) ), does not hold C ( . P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are independent D ( . P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint | 12 |

732 | The odds in favour of India winning any cricket match is ( 2: 3 . ) What is the probability that if India plays 5 matches, it wins exactly 3 of them? ( ^{mathbf{A}} cdot_{^{5}} C_{3}left(frac{2}{5}right)^{2}left(frac{3}{5}right)^{3} ) ( ^{mathrm{B}} cdot_{^{5}} C_{3}left(frac{2}{3}right)^{2}left(frac{1}{3}right)^{3} ) ( ^{mathbf{c}} cdot_{^{5}} C_{3}left(frac{2}{5}right)^{3}left(frac{3}{5}right)^{2} ) ( ^{mathrm{D} cdot}^{5} C_{3}left(frac{2}{3}right)^{2}left(frac{1}{3}right)^{2} ) | 12 |

733 | A bouquet from 11 different flowers is to be made so that it contains not less then three flowers. Then the number of the different ways of selecting flowers to from the bouquet A . 1972 в. 1952 c. 1981 D. 1947 | 12 |

734 | Rahim takes out all the hearts from the cards. What is the probability of Picking out a card that is not a heart. | 12 |

735 | Seven digits from the numbers 1,2,3,4 5,6,7,8,9 are written down nonrepeatedly in a random order to form a seven digit number. The probability that this seven digit number is divisible by 9 is ( A cdot frac{2}{9} ) B. ( frac{7}{36} ) ( c cdot frac{1}{9} ) ( D cdot frac{7}{12} ) | 12 |

736 | A box contains 6 red balls and 2 black balls. Two balls are drawn at random from it without replacement. if ( x ) denotes the number of red balls drawn, then find ( boldsymbol{E}(boldsymbol{x}) ) | 12 |

737 | Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4 | 12 |

738 | A two digit number is to be formed from the digits ( 0,1,3,4 . ) Repetition of the digits is allowed. Find the probability that number that formed is a – (1) prime number (2) multiple of 4 (3) multiple of 11. | 12 |

739 | Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades Hence find the mean of the distribution | 12 |

740 | A coin is tossed 1000 times with the following frequencies: Head: ( 445, ) Tail: 555 When a coin is tossed at random, what is the probability of getting a head? | 12 |

741 | If ( A ) and ( B ) are independent events such ( operatorname{that} P(A)=0.3 ) and ( P(B)=0.4, ) then find (i) ( P(A text { and } B) ) (ii) ( P(A text { or } B) ) | 12 |

742 | The chance of throwing a total of 3 or 5 or 11 with two dice is. A ( cdot frac{5}{36} ) в. ( frac{1}{9} ) ( c cdot frac{2}{9} ) D. ( frac{19}{36} ) | 12 |

743 | Assume that the chances of a patient having a heart attack are ( 40 % ). It is also assumed that a meditation and yoga course reduce the risk of heart attack by ( 30 % ) and the prescription of certain drugs reduces its chances by ( 25 % ). At a time a patient can choose any one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga? | 12 |

744 | Two dice are thrown. The probability that the sum of the numbers coming up on them is 9 , if it is known that the number 5 always occurs on the first die, is A ( cdot frac{1}{6} ) B. ( frac{1}{3} ) ( c cdot frac{1}{2} ) D. ( frac{5}{6} ) | 12 |

745 | A pack of cards was found to contain only 51 cards. If first 13 cards, which are examined, are all red, then find the probability that the missing cards is black? A ( cdot 2 / 3 ) в. ( 1 / 3 ) c. ( 2 / 9 ) D. ( 1 / 6 ) | 12 |

746 | The p. ( m ). ( f ). ( X ) -number of major defects randomly selected appliance of a certain type is : [ x-x ] ( begin{array}{lllll}text { P(a) } & text { 0.08 } & text { 0.15 } & text { 0.45 } & text { 0.27 }end{array} ) Find the expected value and standard deviation of ( X ) | 12 |

747 | If two events ( A ) and ( B ) are such that ( boldsymbol{P}(overline{boldsymbol{A}})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3}, ) then ( boldsymbol{P}left(frac{boldsymbol{B}}{boldsymbol{A} cup overline{boldsymbol{B}}}right) ) is equal to A ( cdot frac{5}{8} ) B. ( frac{7}{8} ) ( c cdot frac{3}{8} ) D. | 12 |

748 | A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8 , given that the red die resulted in a number less than 4 | 12 |

749 | Bag ( A ) contains 2 white and 3 red balls and bag ( B ) contains 4 white and 5 red balls. One ball is drawn at random from one of the bag is found to be red. Find the probability that it was drawn from bag ( boldsymbol{B} ) ( A cdot frac{3}{8} ) в. ( frac{25}{52} ) ( c cdot frac{1}{8} ) D. ( frac{3}{14} ) | 12 |

750 | A fair coin and an unbiased die are tossed. Let ( A ) be the event ‘head appears on the coin’ and ( B ) be the event ‘3 on the die’. Check whether ( A ) and ( B ) are independent events or not. A. True B. False | 12 |

751 | Tickets numbered from 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the drawn ticket has a number which is divisible by both 2 and ( 6 ? ) A ( cdot frac{1}{2} ) B. ( frac{2}{5} ) ( c cdot frac{8}{15} ) D. | 12 |

752 | Two events ( A ) and ( B ) are such that ( P(A)=frac{1}{4}, P(B)=frac{1}{2} ) and ( P(B mid A)=frac{1}{2} ) Consider the following statements ( (I) P(bar{A} mid bar{B})=frac{3}{4} ) ( (I I) A ) and ( B ) are mutually exclusive ( (I I I) P(bar{A} mid bar{B})+P(A mid bar{B})=1 ) Then A. Only I is correct B. Only I and II are correct c. only ( I ) and ( I I I ) are correct D. only II and III are correct | 12 |

753 | A bag contains 4 balls. Two balls are taken out without replacement and found to be white. Find the probability that all the balls of the bag are white. | 12 |

754 | You have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, if the probability of getting a non-blue sector is ( frac{4}{m} . ) Then, the value of ( m ) is ( A, 5 ) B. 4 ( c . ) ( D ) | 12 |

755 | 29. A box contains 15 green and 10 yeilow balls. If 10 L are randomly drawn, one-by-one, with replacement the variance of the number of green balls drawn is cement, then [JEE M 2017 (c) 6 (d) 4 | 12 |

756 | ( A, B ) and ( C ) are three mutually exclusive and exhaustive events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{2} boldsymbol{P}(boldsymbol{B})=mathbf{3} boldsymbol{P}(boldsymbol{C}) ) What is ( boldsymbol{P}(boldsymbol{B}) ) ? A ( .6 / 11 ) B. ( 6 / 22 ) c. ( 1 / 6 ) D. ( 1 / 4 ) | 12 |

757 | A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man? | 12 |

758 | Before a race the chances of three runners, ( A, B, C, ) were estimated to be proportional to 5,3,( 2 ; ) but during the race ( A ) meets with an accident which reduces his chance to one-third. What are now the respective chances of ( boldsymbol{B} ) and ( C ? ) | 12 |

759 | The probability of an ( _{—–} ) is greater than or equal to 0 and less than or equal to 1. A. space B. experiment c. sample D. event | 12 |

760 | Two dice are thrown. The events ( A, B, C, D, E ) and ( F ) are described as follows: ( A= ) Getting an even number on the first die. ( B= ) Getting an odd number on the first die. ( C= ) Getting at most 5 as sum of the number on the two dice. ( D= ) Getting the sum of the numbers on the dice greater than 5 but less than 10 . ( boldsymbol{E}=operatorname{Getting} ) at least 10 as the sum of the numbers on the dice. ( boldsymbol{F}= ) Getting an odd number on one of the dice Describe the following events: ( A ) and ( B, B ) or ( C, B ) and ( C, A ) and ( E, A ) or ( F, A ) and ( boldsymbol{F} ) | 12 |

761 | ( A, B, C ) are any three events. If ( P(S) ) denotes the probability of ( S ) happening, ( operatorname{then} boldsymbol{P}(boldsymbol{A} cap(boldsymbol{B} cup boldsymbol{C}))= ) A ( cdot P(A)+P(B)+P(C)-P(A cap B)-P(A cap C) ) B . ( P(A)+P(B)+P(C)-P(B) P(C) ) C ( cdot P(A cap B)+P(A cap C)-P(A cap B cap C) ) D. None of these | 12 |

762 | Let A and B be two events such that P(AUB)=1 P(AO B)= and P(A)= =, where A stands for complement of event A. Then events A and B are (a) equally likely and mutually exclusive [2005] (b) equally likely but not independent (c) independent but not equally likely (d) mutually exclusive and independent | 12 |

763 | Probability of an event is always less than or equal to A. 0 B. 1 ( c cdot> ) D. None of these | 12 |

764 | Jiah is doing an experiment in her math class. She flips four coins In the air. What is most likely to happen? A. Two of the coins will be heads and two will be tails B. Three of the coins will be heads and one will be tail c. Allfour coins willbe heads D. None of the coins willbe heads | 12 |

765 | The probability distribution of a random variable ( X ) is given below ( boldsymbol{X}=boldsymbol{x} ) ( begin{array}{ll}-1.5 & -0.5end{array} ) ( mathbf{0 . 5} ) ( P[X= ) ( X] )( quad 0.05 ) 0.25 0.15 The variance of ( boldsymbol{X} ) is A . 1.6 B. 0.24 c. 0.84 D. 0.75 | 12 |

766 | When the dice are thrown, the event ( E=4, ) then this event is called A. compound event B. simple event c. impossible event D. complementary event | 12 |

767 | The probability of a man hitting the ( operatorname{target} ) is ( frac{1}{4} . ) If he fires 7 times, the probability of hitting the target exactly six times is ( ^{mathrm{A}} cdot_{^{7}} C_{5}left(frac{1}{4}right)^{6}left(frac{3}{4}right) ) ( ^{mathrm{B} cdot}^{7} C_{6}left(frac{3}{4}right)^{6}left(frac{1}{4}right) ) ( ^{mathbf{c}} cdot_{7} C_{6}left(frac{1}{4}right)^{6}left(frac{3}{4}right) ) ( ^{mathrm{D} cdot}^{7} C_{6}left(frac{1}{2}right)^{6}left(frac{1}{2}right) ) | 12 |

768 | The PDF of variable x: number of times sum 6 appears on in two throw of a pair of dice is [ begin{array}{cc} mathbf{0} & mathbf{1} end{array} ] ( p(x) ) then values of ( a, b, c ) are. A ( cdot a=frac{2}{36}, b=frac{3}{36}, c=frac{5}{36} ) В. ( a=frac{961}{36}, b=frac{310}{36}, c=frac{25}{36} ) ( ^{mathbf{C}} cdot_{a}=frac{961}{1269}, b=frac{310}{1296}, c=frac{25}{1296} ) D. ( a=frac{91}{36}, b=frac{30}{36}, c=frac{25}{36} ) | 12 |

769 | If ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})=1 ; ) then which of the following option explains the event ( boldsymbol{A} ) and ( B ) correctly? A. Event ( A ) and ( B ) are mutually exclusive, exhaustive and complementary events B. Event ( A ) and ( B ) are mutually exclusive and exhaustive events C. Event ( A ) and ( B ) are mutually exclusive and complementary events D. Event ( A ) and ( B ) are exhaustive and complementary events | 12 |

770 | The probabilities of solving a problem by three students ( A, B ) and ( C ) are ( frac{1}{2}, frac{3}{4} ) and ( frac{1}{4} ) respectively. The probability that the problem will be solved is ( ^{A} cdot frac{3}{32} ) в. ( frac{3}{16} ) c. ( frac{29}{32} ) D. None of the above | 12 |

771 | A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is: A ( cdot frac{2}{13} ) в. ( frac{11}{13} ) c. ( frac{4}{13} ) D. ( frac{8}{13} ) | 12 |

772 | Given two independent events ( A, B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} ) Determine ( boldsymbol{P}(boldsymbol{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{n} boldsymbol{o} boldsymbol{B} boldsymbol{B}) ) | 12 |

773 | Suppose values taken by a variable are such that ( a leq x, leq b ) where ( x, ) denote the value of ( x ) in the ( i^{t h} ) class for ( i= ) ( l, 2, cdots n, ) then A ( cdot a^{2} leq operatorname{Var}(x) leq b ) B cdot ( a^{2} leq a^{2}(x) leq b^{2} ) ( ^{mathrm{c}} cdot frac{a^{2}}{4} leq operatorname{Var}(x) ) D. ( operatorname{Var} x leq(b-a)^{2} ) | 12 |

774 | Which of the following is an experiment? A. Tossing a coin B. Rolling a single 6 – sided dice c. choosing a marble from a jar D. All of the above | 12 |

775 | There are n different object ( 1,2,3, ldots n ) distributed at random in n boxes ( A_{1}, A_{2}, A_{3}, cdots A_{N} . ) Find the probability that two objects are placed in the boxes corresponding to their number. A . в. ( frac{1}{2} ) ( c cdot frac{1}{3} ) D. ( frac{2}{3} ) | 12 |

776 | An ordinary pack of 52 cards is well shuffled. The top card is then turned over. What is the probability that the top card is a red card. | 12 |

777 | Sample space for experiment in which two coins are tossed is A . 8 B. 4 ( c cdot 2 ) D. None of these | 12 |

778 | 7 white balls and 3 black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals A ( cdot frac{1}{2} ) в. ( frac{7}{15} ) c. ( frac{2}{15} ) D. | 12 |

779 | Two men hit at a target with probabilities ( frac{1}{2} ) and ( frac{1}{3} ) respectively. What is the probability that exactly one of them hits the target? A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{6} ) D. ( frac{2}{3} ) | 12 |

780 | If ( boldsymbol{P}left(boldsymbol{E}_{k}right)=boldsymbol{C} ) for ( mathbf{0} leq boldsymbol{k} leq boldsymbol{n}, ) then the probability that ( X ) is the only student to pass the examination is A ( .3 / 4 n ) B. ( 2 /(n+1) ) c. ( 2 / n(n+1) ) D. ( 3 / n(n+1) ) | 12 |

781 | A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king. | 12 |

782 | A bag contains 5 red and 8 white balls. If a ball is drawn at random from the bag, what is the probability that it will be: (i) White ball, (ii) Not a white ball? | 12 |

783 | If the mean and variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes of that binomial variate ( boldsymbol{X}, ) is A ( cdot frac{1}{2} ) в. ( frac{219}{256} ) c. ( frac{37}{256} ) D. ( frac{7}{64} ) | 12 |

784 | Assertion Let ( A, B ) and ( C ) be three events such that ( boldsymbol{P}(boldsymbol{C})=mathbf{0} ) ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})=mathbf{0} ) Reason ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 12 |

785 | A bag contains 3 white, 3 black, and 2 red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red. A ( cdot frac{1}{4} ) B. ( frac{3}{4} ) ( c cdot frac{1}{3} ) D. None of these | 12 |

786 | A die is thrown, a man ( C ) gets a prize of Rs. 5 if the die turns up 1 and gets a prize of Rs. 3 if the die turns up ( 2, ) else he gets nothing, A man ( A ) whose probability of speaking the truth is ( frac{1}{2} ) tells ( C ) that the die has turned up 1 and another man ( B ) whose probability of speaking the truth is ( frac{2}{3} ) tells ( C ) that the die has turned up 2. Find the expectation value of ( boldsymbol{C} ) | 12 |

787 | If ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{7}}{mathbf{1 3}}, boldsymbol{P}(boldsymbol{B})=frac{mathbf{9}}{mathbf{1 3}}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) 2 – then find ( (mathrm{A} mid mathrm{B}) ) 13 | 12 |

788 | A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is : A ( cdot frac{10}{3^{5}} ) в. ( frac{17}{3^{5}} ) c. ( frac{13}{3^{5}} ) D. ( frac{11}{3^{5}} ) | 12 |

789 | -I contains 3 red and 4 black balls Bag while another Bag -ll contains 5 red and 6 black b alls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag -II. | 12 |

790 | For the probability distribution function of random variable ( X, x_{1}, x_{2}, x_{3}, dots x_{n} ) are the values ( X ) takes, and ( pleft(x_{i}right) ) denote the probability of ( x_{i} ) then which one of the following is true.? This question has multiple correct options ( mathbf{A} cdot pleft(x_{i}right)>0 ) в. ( pleft(x_{i}right)<0 ) ( mathbf{c} cdot sum pleft(x_{i}right)=1 ) D. ( sum x_{i}=1 ) | 12 |

791 | In a survey of 500 ladies, it was found that 180 like coffee while rest of the ladies dislike it. From these ladies, one is chosen at random. What is the probability that the chosen lady dislikes coffee? | 11 |

792 | One hundred identical coins, each with probability ( p, ) of showing up heads are tossed. If ( 0<p<1 ) and the probability of heads showing on 50 coins is equal to that of the heads showing in 51 coins, then the value of ( p ) is A ( cdot frac{1}{2} ) в. ( frac{49}{101} ) c. ( frac{50}{101} ) D. ( frac{51}{101} ) | 12 |

793 | If ( phi ) represents an impossible event then ( boldsymbol{P}(phi)=? ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot phi ) D. – | 12 |

794 | Two dice are thrown: ( P ) is the event that the sum of the scores on the uppermost faces is a multiple of 6 ( Q ) is the event that the sum of the scores on the uppermost faces is at least 10 ( R ) is the event that same scores on both dice. Which of the following pairs is mutually exclusive? | 12 |

795 | ( A ) and ( B ) are two independent events. The probability that both ( A ) and ( B ) occur is ( 1 / 6 ) and the probability that at least one of them occurs is ( frac{2}{3} . ) The probability of the occurrence of ( boldsymbol{A}=ldots ldots ldots ) if ( boldsymbol{P}(boldsymbol{A})= ) ( 2 P(B) ) ( A cdot frac{2}{9} ) в. 4 ( c cdot frac{5}{9} ) D. ( frac{5}{18} ) | 12 |

796 | Five ordinary dies are rolled at random and the sum of numbers shown is 16 What is the probability that the number shown on each is any one from 2,3,4 or ( mathbf{5} ? ) A ( cdot frac{9}{49} ) B. ( frac{3}{49} ) c. ( frac{2}{49} ) D. None of these | 12 |

797 | 100 tickets are numbered as 00,01,02 ( ldots .09,10,11,12, ldots .99 . ) Out of them, one ticket is drawn at random. The probability that the sum of the digits of the number on the ticket is 9 is A. ( frac{7}{100} ) в. ( frac{9}{100} ) c. ( frac{1}{10} ) D. ( frac{1}{100} ) | 12 |

798 | Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( P(A / B) ) | 12 |

799 | If ( mathrm{E} & mathrm{F} ) are events with ( boldsymbol{P}(boldsymbol{E}) leq boldsymbol{P}(boldsymbol{F}) & ) ( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})>0, ) then A. occurrence of ( E Rightarrow ) occurrence of ( F ) B. occurrence of FRightarrow occurrence of E c. non occurrence of ( E Rightarrow ) non occurrence of ( F ) D. none of the above implications holds | 12 |

800 | A bag contains 8 red, 6 white and 4 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is (i) red or white (ii) not black neither white nor black | 12 |

801 | 3. A dice is tossed 5 times. Getting an odd numbe a success. Then the variance of distribution o (2) 8/3 (6) 318 (c) 4/5 (d) 5/4 The mean and blo y having Jetting an odd number is considered Then the variance of distribution of success is 2002 | 12 |

802 | The probability that Chakri passes in mathematics is ( frac{2}{3} ) and the probability that he passes in English is ( frac{4}{9} . ) If the probability of passing both courses is ( frac{1}{4}, ) then the probability that Chakri wil pass in at least one of these subjects is ( mathbf{3 1} ) 立 ( overline{mathbf{3 6}} ) A . True B. False c. Ambiguous D. Data Insufficient | 12 |

803 | If ( A ) and ( B ) are two events in a sample space ( S ) such that ( P(A) neq 0, ) then ( Pleft(frac{B}{A}right)= ) A ( cdot P(A) cdot P(B) ) в. ( frac{P(A cap B)}{P(B)} ) c. ( frac{P(A cap B)}{P(A)} ) D ( cdot P(B) ) | 12 |

804 | A balloon vendor has 2 red,3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets: (i) a red balloon (ii) a blue balloon (iii) a green balloon. | 12 |

805 | A man is know to speak the truth 3 out if 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is: A ( cdot frac{3}{8} ) B. ( frac{1}{5} ) ( c cdot frac{3}{4} ) D. None of these | 12 |

806 | In a single throw of a die, the events {1,2},{2,3} are mutually exclusive. Write 1 if true and 0 if false. | 12 |

807 | If ( A ) and ( B ) are two events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= ) ( mathbf{0 . 1 5}, operatorname{then} boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= ) A . 0.6 B. 0.8 c. 1.2 D. 1. | 12 |

808 | The probabilities of ( x, y ) and ( z ) becoming manager are ( frac{4}{9}, frac{2}{9} & frac{1}{3} ) respectively. The probabilities that the bonus scheme will be introduced if ( x, y ) and ( z ) become managers are ( frac{3}{10}, frac{1}{2} & frac{2}{5} ) respectively. Find (i) What is the probatility that the bonus scheme will be introduced? (ii) if the bonus scheme has teen introduced, What is the probability that the manager appointed wax ( x ? ) | 12 |

809 | If for a binomial distribution ( bar{x}=frac{6}{5} ) and the difference between mean and variance is ( frac{6}{25} . ) The number of trials is A . 8 B. 7 ( c .6 ) D. | 12 |

810 | If ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{3}}{boldsymbol{4}}, boldsymbol{P}left(boldsymbol{B}^{prime}right)=frac{1}{3} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{P}(boldsymbol{A} cap ) ( B)=frac{1}{2} ) then find ( P(A cup B) ) A ( cdot frac{5}{12} ) в. ( frac{6}{12} ) c. ( frac{7}{12} ) D. ( frac{11}{12} ) | 12 |

811 | A pair of number cubes is rolled up.What is the probability that the sum is odd given that the sum is greater than or equal to 9 A ( cdot frac{1}{6} ) в. ( frac{3}{28} ) ( c cdot frac{2}{6} ) D. | 12 |

812 | The probability of picking a number which ends with 3 from first 100 natural numbers is A . ( 0 . ) B. 0.3 c. 0.13 D. none | 12 |

813 | A coin is tossed. Find the total number of elementary events and also the total number events associated with the random experiment. | 12 |

814 | Two unbiased dice are rolled once. Find the probability of getting a doublet. A ( cdot frac{1}{6} ) B. ( frac{3}{4} ) ( c cdot frac{2}{3} ) D. | 12 |

815 | 7. When a die is thrown, list the outcomes of an event of getting (1) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5. | 11 |

816 | A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen? A ( cdot frac{2}{9} ) в. ( frac{1}{14} ) c. ( frac{2}{63} ) D. ( frac{2}{14} ) | 12 |

817 | One of the two boxes, box ( boldsymbol{I} ) and box ( boldsymbol{I} boldsymbol{I} ) was selected at random and balls are drawn randomly out of this box. The ball was found to be red.If the probability that this red ball was drawn from box ( I I ) is ( frac{1}{3}, ) then the correct option options with the possible values of ( n_{1}, n_{2}, n_{3} ) and ( n_{4} ) is (are) This question has multiple correct options ( mathbf{A} cdot n_{1}=3, n_{2}=3, n_{3}=5, n_{4}=15 ) B . ( n_{1}=3, n_{2}=6, n_{3}=10, n_{4}=50 ) C ( . n_{1}=8, n_{2}=6, n_{3}=5, n_{4}=20 ) D ( cdot n_{1}=6, n_{2}=12, n_{3}=5, n_{4}=20 ) | 12 |

818 | 2. Assertion: Weighing of an apple is an example of random experiment. Reason: A random experiment is that in which outcomes may differ each time when we perform an experiment. | 11 |

819 | If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability ( left.frac{1}{2}right) ) | 12 |

820 | In a class of 50 boys, 35 like horror movies, 30 like war movies and 5 like neither. Find the number of those that like both. A . 20 B . 25 c. 15 D. 28 | 12 |

821 | Assertion If the independent events ( boldsymbol{A} & boldsymbol{B} ) are such that ( mathbf{0}<boldsymbol{P}(boldsymbol{A})<mathbf{1}, mathbf{0}<boldsymbol{P}(boldsymbol{B})< ) 1, then ( A & B ) can not be mutually exclusive. Reason Two events ( A & B ) can not be mutually exclusive, if ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) neq mathbf{0} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

822 | Ta U 1 ) (u 8/9. given that the events A and B are such that 16. It is given that P(A) = 1, PCAB) = and PCB | 4) = . Then P(B) is [2008] is thrown Let A be the event that the number obtain | 12 |

823 | ( A ) and ( B ) are two events where ( P(A)= ) 0.25 and ( P(B)=0.5 . ) The probability of both happening together is 0.14 . The probability of both ( A ) and ( B ) not happening is A . 0.39 B. 0.25 c. 0.11 D. none of these | 12 |

824 | A fair die is rolled. Find the probability of getting the number 5 A ( cdot frac{1}{6} ) в. ( frac{5}{6} ) ( c cdot frac{2}{6} ) D. ( frac{3}{6} ) | 12 |

825 | If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) . boldsymbol{A} ) and ( boldsymbol{B} ) are two non-mutually exclusive events then A. ( A ) and ( B ) are necessarily same events в. ( P(A)=P(B) ) c. ( P(A cap B)=P(A) P(B) ) D. all the above | 12 |

826 | Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of ( X ) | 12 |

827 | The mode of the binomial distribution for which mean and standard deviation are 10 and ( sqrt{5} ) respectively, is A. 7 B. 8 ( c .9 ) D. 10 | 12 |

828 | The probability of an event is A. always more than 1 B. always less than 1 c. always equal to D. always negative | 12 |

829 | Three fair dice are thrown. The probability of getting a sum 6 or less on the three dice is ( ^{A} cdot frac{7}{12} ) в. ( frac{5}{54} ) c. ( frac{19}{216} ) D. ( frac{11}{108} ) | 12 |

830 | Let ( A ) and ( B ) be two independent events. The probability that both ( A ) and ( B ) happen is ( frac{1}{12} ) and the probability that neither ( A ) nor ( B ) happen is ( 1 / 2 ).If the sum of probabilities of occurence of ( boldsymbol{A} ) and ( B ) is ( frac{k}{12}, ) then the value of ( k ) is | 12 |

831 | ( A ) and ( B ) are seeking admission into IIT. If the probability for ( A ) to be selected is 0.5 and that both to be selected is ( 0.3, ) them is it possible that, the probability of ( B ) to be selected is 0.9 ( ? ) | 12 |

832 | Two persons ( A ) and ( B ) are throwing an unbiased six faced die alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, the probabilities of ( A ) and ( B ) to win the same are respectively A ( cdot frac{6}{11}, frac{5}{11} ) B . ( frac{5}{11}, frac{6}{11} ) c. ( frac{8}{11}, frac{3}{11} ) D. ( frac{3}{11}, frac{8}{11} ) | 12 |

833 | An urn contains 4 red and 7 blue balls. Find the probability of getting Blue balls | 12 |

834 | A quadratic equation ( a x^{2}+b x+c=0 ) with distinct coefficients is formed. It a b, c are chosen from the numbers 2,3,5 then the probability that the equation has real roots is A ( cdot frac{1}{3} ) B. ( frac{2}{5} ) ( c cdot frac{1}{4} ) D. E ( cdot frac{2}{3} ) | 12 |

835 | Two coins are tossed once. Find the probability of getting: (i) 2 heads (ii) at least 1 tail | 12 |

836 | The length of similar components produced by a company is approximated by a normal distribution model with a mean of ( 5 mathrm{cm} ) and a standard deviation of ( 0.02 mathrm{cm} . ) If a component is chosen at random.what is the probability that the length of this component is between 4.98 and 5.02 ( mathrm{cm} ? ) ( mathbf{A} cdot 0.5826 ) B . 0.6826 c. 0.6259 D. 0.6598 | 12 |

837 | 4. Getting a number less than 1 when a die is thrown. | 10 |

838 | The events ( E_{1}, E_{2}, ldots ldots . . ) represents the partition of the sample space ( S ), if they are: A. pairwise disjoint B. exhaustive c. have non-zero probabilities D. All are correct | 12 |

839 | From a standard deck of cards, one card is drawn. Find the probability that the card is red and a queen A ( cdot frac{1}{2} ) в. ( frac{4}{13} ) c. ( frac{1}{26} ) D. ( frac{12}{13} ) | 12 |

840 | A factory has three machines ( A, B ) and ( C ) which produce 100,200 and 300 items of a particular type daily. The machines produce ( 2 %, 3 % ) and ( 5 % ) defective items respectively. One day when the production was over, an item was picked up randomly and it was found to be defective. Find the probability that it was produced by machine ( A ) | 12 |

841 | Probability of impossible event is ( A cdot 1 ) B. 0 ( c cdot frac{1}{2} ) D. – | 12 |

842 | A number is selected from the set ( {1,2, ) 3,4,5,6,7,8}( . ) What is the probability that it will be the root of the equation ( x^{2}-6 x+8=0 ? ) | 12 |

843 | Assume that the chances of a patient having a heart attack is ( 40 % ). Assuming that a mediation and yoga course reduces the risk of heart attack by ( 30 % ) and prescription of certain drug reduces its chance by ( 25 % ). At a time a patient can choose any one of the two options with equal possibilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of mediation and yoga. Interpret the result and state which of the above stated methods is more beneficial for the patient. | 12 |

844 | If ( A, B ) and ( C ) are three events such that ( P(B)=frac{3}{4}, Pleft(A cap B cap C^{prime}right)=frac{1}{3} ) and ( Pleft(A^{prime} cap B cap C^{prime}right)=frac{1}{3}, operatorname{then} P(B cap C) ) is equal to A ( cdot frac{1}{12} ) B. c. ( frac{1}{15} ) D. | 12 |

845 | There are 30 tickets in a box numbered from 1 to ( 30 . ) A ticket is drawn out at random. Let ( A ) be the event that the number on the ticket is a multiple of 6 Write the sample set ( S ) and outcomes of event ( A ) in set form. | 12 |

846 | A bag contains 6 balls. Two balls are drawn and found to be red. The probability that five balls in the bag are red A ( cdot frac{5}{6} ) в. ( frac{12}{17} ) ( c cdot frac{1}{3} ) D. | 12 |

847 | If ( A ) and ( B ) are events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap ) ( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) ) | 12 |

848 | A coin is tossed ( 2 n ) times. The chance that the number of times one gets head is not equal to the number of times one gets tail is A ( cdot frac{(2 n) !}{(n ! !)^{2}} cdotleft(frac{1}{2}right)^{2} n ) B. ( _{1-} frac{(2 n) !}{(n !)^{2}} ) c. ( _{1-} frac{(2 n) !}{(n !)^{2}} cdot frac{1}{4^{n}} ) D. none of these | 12 |

849 | A coin is tossed three times. Find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) in given cases: ( A=A t ) most two tails, ( B=A t ) least one tail. | 12 |

850 | Two events ( A ) and ( B ) will be independent, if ( mathbf{A} . A ) and ( B ) are mutually exclusive B ( cdot Pleft(A^{prime} B^{prime}right)=[1-P(A)][1-P(B)] ) ( mathbf{c} cdot P(A)=P(B) ) D ( cdot P(A)+P(B)=1 ) | 12 |

851 | Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes. | 12 |

852 | The probability distribution function of a random variable ( boldsymbol{X} ) is given by ( boldsymbol{x}_{i}: quad 0 quad 1 quad 2 ) [ begin{array}{lll} 3 c & 4 c & c-1 end{array} ] where ( c>0 . ) Find ( c ) | 12 |

853 | To know the opinion of the student about the subject statistic, a survey of 200 students was conducted. The data is recorded in the following table opinion 1 Like Dislike No. of Students 65 135 Find the probability that a student chosen at random ( (i) ) likes statistics, ( (i i) ) does not like it. A. [ begin{array}{l} (i) frac{13}{40} \ (i i) frac{19}{40} end{array} ] в. [ (i) frac{27}{40} ] ( (i i) frac{13}{40} ) c. [ (i) frac{17}{40} ] ( (i i) frac{29}{40} ) D. None of these | 12 |

854 | ( 2 n ) boys are randomly divided into two subgroups containing ( n ) boys each. The probability that the two tallest boys are in different groups is A ( . n /(2 n-1) ) B. ( (n-1) /(2 n-1) ) c. ( (n-1) / 4 n^{2} ) D. None of these | 12 |

855 | What is the probability of an event? | 11 |

856 | Three candidates solve a question. Odds in favour of the correct answer are 5 : 2,4: 3 and 3: 4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly? A ( cdot frac{209}{343} ) в. ( frac{134}{343} ) c. ( frac{149}{343} ) D. ( frac{60}{343} ) | 12 |

857 | By examine the chest the chest ( X- ) ray probability that ( T . B ) is detected when a person is actually suffering is ( 0.99 . ) The probability that the doctor diagnoses incorrectly that a person has ( T . B ) on the bases of ( X- ) ray is ( 0.001 . ) In a certain city 1 in 1000 person suffers from ( T . B ) A person is selected at random is diagnoses to have ( T . B ). What is the chance that the actually has ( T . B ? ) | 12 |

858 | A die is thrown twice and the sum of the numbers appearing is observed to be 7 Find the conditional probability that the number 3 has appeared at least once. | 12 |

859 | State which of the following are not the probability distributions of a random variable. Give reasons for your answer. ( (i) ) begin{tabular}{|c|l|l|l|} hline ( mathrm{X} ) & 0 & 1 & 2 \ hline ( mathrm{P}(mathrm{X}) ) & 0.4 & 0.4 & 0.2 \ hline end{tabular} (ii) begin{tabular}{|c|l|l|l|c|l|} hline ( mathrm{X} ) & 0 & 1 & 2 & 3 & 4 \ hline ( mathrm{P}(mathrm{X}) ) & 0.1 & 0.5 & 0.2 & -0.1 & 0.3 \ hline end{tabular} (iii) begin{tabular}{|c|r|l|l|} hline ( mathrm{Y} ) & -1 & 0 & 1 \ hline ( mathrm{P}(mathrm{Y}) ) & 0.6 & 0.1 & 0.2 \ hline end{tabular} (iv) begin{tabular}{|c|l|l|l|l|l|} hline ( mathrm{Z} ) & 3 & 2 & 1 & 0 & -1 \ hline ( mathrm{P}(mathrm{Z}) ) & 0.3 & 0.2 & 0.4 & 0.1 & 0.05 \ hline end{tabular} | 12 |

860 | A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while ( mathrm{Mr} ) Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is: A ( cdot frac{1}{18} ) в. ( frac{1}{9} ) ( c cdot frac{1}{6} ) D. None of these | 12 |

861 | If two events ( A ) and ( B ) are such that ( P(bar{A})=frac{3}{10}, P(B)=frac{2}{5} ) and ( P(A cap ) ( bar{B})=frac{1}{2}, operatorname{then} Pleft(frac{B}{A cup bar{B}}right) ) is A ( cdot frac{1}{2} ) B. ( c cdot frac{1}{4} ) D. | 12 |

862 | A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is ( 0 cdot 4 ) and that lot contains exactly 3 defective articles is ( 0 cdot 6 . ) Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. The probability that testing procedure ends at the twelfth testing is ( frac{11 k}{1900} . ) Find the value of ( k ? ) | 12 |

863 | If ( A & B ) are independent events such ( operatorname{that} P(B)=frac{2}{7}, P(A cup bar{B})=0.8, ) then ( P(A) ) is equal to A . ( 0 . ) B. 0.2 ( c .0 .3 ) D. 0.4 | 12 |

864 | The mean and variance of Binomial Distribution are 4 and 2 respectively, then the probability of success is A ( cdot frac{128}{256} ) в. ( frac{219}{256} ) c. ( frac{37}{256} ) D. ( frac{28}{256} ) | 12 |

865 | A fair die is rolled. Consider events ( boldsymbol{E}= ) ( {1,3,5}, F={2,3} ) and ( G= ) {2,3,4,5} Find (i) ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) ) and ( boldsymbol{P}(boldsymbol{F} mid boldsymbol{E}) ) (ii) ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{G}) ) and ( boldsymbol{P}(boldsymbol{G} mid boldsymbol{E}) ) (iii) ( P((E cup F) mid G) ) and ( P((E cap F) mid G) ) | 12 |

866 | For a binomial distribution if ( boldsymbol{P}=frac{mathbf{2}}{mathbf{3}} ) and ( n=10 ) the probability of mode is ( ^{mathbf{A}} cdot_{^{10}} C_{4}left(frac{1}{3}right)^{7}left(frac{2}{3}right)^{3} ) ( ^{mathrm{B}} cdot_{^{10}} C_{7}left(frac{2}{3}right)^{7}left(frac{1}{3}right)^{3} ) ( ^{c}left(frac{2}{3}right)^{7}left(frac{1}{3}right)^{3} ) ( ^{text {D }}left(frac{1}{3}right)^{7}left(frac{2}{3}right)^{3} ) | 12 |

867 | For three events ( A, B ) and ( C, P ) (exactly one of the events ( A text { occur })=P ) (exactly one of the events ( B text { and } C text { occur })=P ) (exactly one of the events ( C ) or ( A ) occurs) ( =mathrm{p} ) and ( mathrm{P} ) (all the three events occur simultaneously) ( =p^{2}, ) where ( 0<p< ) 1/2. If the probability of at least one of the three events ( A, B ) and ( C ) occurs is ( 11 / 18, ) the value of ( p ) is A ( cdot 1 / 6 ) в. ( 1 / 4 ) c. ( 1 / 5 ) D. ( 1 / 3 ) | 12 |

868 | A box contains 2 silver coins and 4 gold coins and the second box contains 4 silver coins and 3 gold coins. If a coin is selected from one of the box, what is the probability that it is a silver coin. A . 0.3 B. 0.4 c. 0.5 D. 0.6 | 12 |

869 | Assertion ( boldsymbol{P}(boldsymbol{H} / boldsymbol{E})>boldsymbol{P}left(boldsymbol{E} / boldsymbol{H}_{i}right) boldsymbol{P}left(boldsymbol{H}_{i}right), boldsymbol{i}= ) ( mathbf{1}, mathbf{2}, mathbf{3}, dots, boldsymbol{n} . operatorname{Let} boldsymbol{H}_{1}, boldsymbol{H}_{2}, boldsymbol{H}_{3}, dots . . boldsymbol{H}_{n} ) be ( mathbf{n} ) mutually exclusive & exhaustive events with probability ( boldsymbol{P}left(boldsymbol{H}_{boldsymbol{i}}right)>mathbf{0}, boldsymbol{i}= ) ( 1,2,3, dots n . ) Let ( E ) be any other event with ( mathbf{0}<boldsymbol{P}(boldsymbol{E})<mathbf{1} ) Reason ( sum_{i=1}^{n} boldsymbol{P}left(boldsymbol{H}_{i}right)=mathbf{1} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

870 | Assertion For any two events ( A ) and ( B ) ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B})=boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) Reason ( A cap B ) and ( bar{A} cap B ) are mutually exclusive events. A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

871 | Three unbaised coins are tossed find the probability distribution of the number of heads occurring on the topmost faces. | 12 |

872 | Find the mean number of heads in three tosses of a fair coin. | 12 |

873 | The conditional probability that ( X geq 6 ) given the ( X>3 ) equals A ( cdot frac{125}{216} ) в. ( frac{25}{216} ) c. ( frac{5}{36} ) D. ( frac{25}{36} ) | 12 |

874 | If the variance of the random variable ( boldsymbol{X} ) is ( 5, ) then the variance of the random variable ( -mathbf{3} boldsymbol{X} ) is A . 15 B . 45 c. -45 D. 60 | 12 |

875 | One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is A . ( 1 / 2 ) B. ( 1 / 3 ) ( c cdot 2 / 5 ) D. ( 1 / 5 ) | 12 |

876 | A bag contains some white and some black balls, all of which are distinguishable from each other, all combinations of balls being equally likely. The total number of balls in the bag is ( 10 . ) If three balls are drawn at random and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is : A ( cdot frac{14}{55} ) B. ( frac{12}{55} ) c. ( frac{8}{55} ) D. ( frac{2}{11} ) | 12 |

877 | In 15 throws of a die 4 or 5 is considered to be a success. The mean number of success is A . 3 B. 4 ( c .5 ) D. 6 | 12 |

878 | There are 4 horizontal and 6 vertical equispaced lines as shown.lf a rectangle is randomly selected then probability that is a square is ( ^{A} cdot frac{7}{45} ) в. ( frac{13}{45} ) c. ( frac{11}{18} ) ( D ) | 12 |

879 | A lot consists of 144 ball pens of which 20 are defective and others are good. Nuri will buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it (ii) She will not buy it | 12 |

880 | A school has five houses ( A, B, C, D ) and ( E ) A class has 23 students, 4 from house A, 8. from house B, 5 from house C, 2 from house 0 and rest from house ( mathrm{E} ) A single student is selected at random ,to be the class monitor. The probability that the selected student is not from ( A ), Band C is? ( mathbf{A} cdot frac{4}{23} ) B. ( frac{6}{23} ) ( c cdot frac{8}{23} ) D. ( frac{17}{23} ) | 12 |

881 | There are 7 defective items in a sample of 35 items. Find the probability that an item chosen at random is non-defective. | 12 |

882 | A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made at random from the bag without replacements. Find the probability that the first draw yields 3 white balls and the second draw 3 red balls. | 12 |

883 | If ( A ) and ( B ) are arbitrary events, then ( mathbf{A} cdot P(A cap B) geq P(A)+P(B) ) B ( cdot P(A cap B) leq P(A)+P(B) ) C ( cdot P(A cap B)=P(A)+P(B) ) D. none of these | 12 |

884 | Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3 ‘. | 12 |

885 | When a coin is tossed at random, then the probability of getting a head is A . 0 B. ( frac{1}{2} ) ( c .1 ) D. 2 | 12 |

886 | 15 coupons are numbered ( 1,2,3, dots, 15 ) respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is ( ^{A} cdotleft(frac{9}{16}right)^{6} ) ( ^{mathrm{B}}left(frac{8}{15}right)^{7} ) ( ^{c}left(frac{3}{5}right)^{7} ) D. ( frac{9^{7}-8^{7}}{15^{7}} ) | 12 |

887 | Suppose ( X ) has a binomial distribution with ( n=6 ) and ( p=frac{1}{2} . ) Show that ( X=3 ) is the most likely outcome. | 12 |

888 | Let ( A ) and ( B ) be two events such that ( P(overline{A cup B})=frac{1}{6}, P(A cap B)=frac{1}{4} ) and ( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for the complement of the event A. Then the events ( A ) and ( B ) are? A. Independent but not equally likely B. Independent and equally likely c. Mutually exclusive and independent D. Equally likely but not independent | 12 |

889 | If ( A, B ) are two events with ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 5} ) then find the value of ( boldsymbol{P}left(boldsymbol{A}^{c}right)+boldsymbol{P}left(boldsymbol{B}^{c}right) ) | 12 |

890 | If atleast one child in a family with 3 children is a boy then the probability that 2 of the children are boys, is ( A cdot frac{3}{7} ) B. ( frac{4}{7} ) ( c cdot frac{1}{3} ) D. ( frac{3}{8} ) | 12 |

891 | 10. If E and F are the complementary events of events E and Frespectively and if 0 <P(F)< 1, then (1998 – 2 Marks) (a) P(E/F) + P(E / F)=1 (b) P(E/F) + P(EIF)=1 (c) P(Ē / F) + P(E/F)=1 (d) P(EIF)+P(EIF)=1 | 12 |

892 | Nayan tosses a coin thrice. Find the probability of getting a) exactly 2 heads and b) at most 2 tails | 12 |

893 | Out of 800 families with 4 children each, the expected number of families having 2 boys and 2 girls A. 100 в. 200 c. 300 D. 400 | 12 |

894 | The probability that ( boldsymbol{P} cap boldsymbol{Q}=boldsymbol{A} ) contains just one element, is ( ^{mathrm{A}} cdot_{n}left(frac{3}{4}right)^{n} ) B. ( left(frac{1}{4}right)^{n} ) c. ( frac{n}{3}left(frac{1}{2}right)^{n} ) D. ( left(frac{3}{4}right)^{n} ) | 12 |

895 | How many play cricket only? | 12 |

896 | A pair of dice is thrown 4 times. If getting a total of 9 in a single throw is considered as a success then find the mean and variance of successes. | 12 |

897 | A bag ( A ) contains 10 white and 3 black balls. Another bag ( B ) contains 3 white and 5 black balls. Two balls are transferred from bag ( A ) and put in the bag ( B ) and a ball is drawn from bag ( B ) Find the probability that the ball drawn is white ball. | 12 |

898 | f ( n(A)=18, n(B)=12, ) and ( A cap B= ) ( emptyset, operatorname{then} n(A cup B)= ) ( A cdot 6 ) B. 12 ( c .30 ) D. 20 | 12 |

899 | Two different families ( A ) and ( B ) are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family ( B ) is ( frac{1}{12}, ) then the number of children in each family is? A .4 B. 6 ( c .3 ) ( D ) | 12 |

900 | Probability that ( A ) speaks truth is ( frac{4}{5} . A ) coin is tossed. A reports that a head appears. The probability that actually there was head is A ( cdot frac{4}{5} ) B. ( frac{1}{2} ) c. ( frac{1}{5} ) D. ( frac{2}{5} ) | 12 |

901 | In a school, ( frac{5}{8} ) of the total students are girls. If the number of girls is 120 more than that of the boys. What is the strength of the school? how many boys are there? A .160 в. 120 c. 100 D. 180 | 12 |

902 | How many coins are to be tossed at once to get 64 outcomes in total? | 12 |

903 | In a hostel, ( 60 % ) of the students read Hindi news paper, ( 40 % ) read English news paper and ( 20 % ) read both Hindi and English news papers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English news papers. (b) If she reads Hindi news paper, find the probability that she reads English news paper (c) If she reads English news paper, find the probability that she reads Hindi news paper. A ( .0 .56,0.78,0.76 ) в. 0.20,0.33,0.50 ( c .0 .65,0.45,0.34 ) D. 0.56,0.56,0.65 | 12 |

904 | Shekar is one member of a group of 5 persons. If 3 out of these 5 persons is to be chosen for a committee, find the probability of Shekar being in the committee | 12 |

905 | The probability that a number selected at random from the numbers ( mathbf{1}, mathbf{2}, mathbf{3} dots dots mathbf{1 5} ) is a multiple of ( mathbf{4} ) is A ( cdot frac{4}{15} ) в. ( frac{2}{15} ) c. ( frac{1}{15} ) D. | 12 |

906 | If the variance of the random variable ( boldsymbol{X} ) is ( 4, ) then the variance of the random variable ( 5 X+10 ) is A. 100 B. 10 c. 50 D. 25 | 12 |

907 | STATEMENT – 1: Dependent events are those in which the outcome of one does not affect and is not affected by the other. STATEMENT – 2 : Dependent events are those in which the outcome of one affects and is affected by the other. A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement- – B. Statement-1 is True, Statement- 2 is True: Statement 2 is NOT a correct explanation for Statement- c. statement- 1 is True, Statement – 2 is False D. Statement – 1 is False, Statement- 2 is True | 12 |

908 | A man take a step forward with probability 0.4 and backward with probability ( 0.6 . ) The probability that at the end of eleven steps he is one step away from the starting point, is A . 0.37 в. 0.57 c. 0.3 D. None of these | 12 |

909 | The number of ways in which 6 men can be arranged in a row, so that three particular men are consecutive, is A ( .4 ! times 3 ! ) в. ( 4 ! ) c. ( 3 ! times 3 ! ) D. none of these | 12 |

910 | If ( A ) and ( B ) are two event such that ( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then ( ^{mathbf{A}} cdot P(A cup B) geq frac{3}{4} ) В. ( P(bar{A} cap B) leq frac{1}{4} ) c. ( frac{3}{8} leq P(A cap B) leq frac{5}{8} ) D. All of these | 12 |

911 | A number consists of 7 digits whose sum is ( 59 ; ) prove that the chance of its being divisible by 11 is ( frac{4}{21} ) | 12 |

912 | If ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{boldsymbol{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} ) and ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} operatorname{then} boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is A ( cdot frac{1}{12} ) B. c. ( frac{1}{15} ) ( D ) | 12 |

913 | A card is drawn at random from a well shuffled pack of 52 cards. The probability that the cards drawn is neither a red card nor a queen is A ( cdot frac{6}{13} ) в. ( frac{5}{13} ) c. ( frac{4}{13} ) D. ( frac{2}{13} ) | 12 |

914 | Cards marked with the numbers 2 to 101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is less than 14 A ( cdot frac{3}{27} ) в. ( frac{3}{29} ) ( c cdot frac{3}{25} ) D. ( frac{3}{22} ) | 12 |

915 | A committee of 4 students is selected at random from a group consisting of 8 boys and 4 girls. Given that there is at least one girl in the committee, the probability that there are exactly 2 girls in the committee is A ( cdot frac{168}{4558} ) B. ( frac{85}{99} ) ( mathbf{c} cdot frac{_{5}}{165} ) D. ( frac{14}{999} ) | 12 |

916 | A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment? | 12 |

917 | The G.M of the numbers ( 3^{1}, 3^{2}, 3^{3}, ldots, 3^{3 n} ) is A ( cdot frac{n}{2} ) в. ( frac{3 n}{2} ) c. ( frac{3 n+1}{2} ) D. ( frac{n+1}{2} ) | 12 |

918 | Which of the following is an outcome? A. Rolling a pair of dice B. Landing on red c. choosing 2 marbles from a jar D. None of the above | 12 |

919 | The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is ( 0.1 . ) If the probability of passing the English examination is 0.75 What is the probability of passing the Hindi examination | 12 |

920 | In a survey conducted among 400 students of ( X ) standard in Pune district, 187 students offered to join Science faculty after ( X ) standard and 125 students offered to join Commerce faculty after ( X ). If a student is selected at random from this group, find the probability that the student prefers Science or Commerce faculty. | 12 |

921 | At a certain university, ( 4 % ) of men are over 6 feet tall and ( 1 % ) of women are over 6 feet tall. The total student population is divided in the ratio 3: 2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman? ( A cdot frac{3}{11} ) В. ( frac{5}{11} ) ( c cdot frac{7}{11} ) D. none of these | 12 |

922 | Two cards are drawn simultaneously from a well shuffled pack of 52 cards. The expected number of aces is? ( ^{A} cdot frac{1}{221} ) в. ( frac{3}{131} ) c. ( frac{2}{113} ) D. ( frac{1}{131} ) | 12 |

923 | Find ( boldsymbol{A} ) or ( boldsymbol{B} ) | 12 |

924 | In bridge game of playing cards, 4 players are distributed one card each by turn so that each player gets 13 cards. Find out the probability of a specified player getting a black ace and a king. This question has multiple correct options A ( cdot p=frac{82251}{978775} ) В. ( quad p=frac{164502}{978775} ) C ( quad p=frac{329004}{978775} ) D. ( _{p}=frac{82251}{1957550} ) | 12 |

925 | The probability of student ( A ) passing an examination is ( 2 / 9 ) and of students, ( B ) passing is ( 5 / 9 . ) Assuming the two events: ( A ) passes’. ( B ) passes’ as independent, find the probability of only ( A ) passing the examination | 12 |

926 | A bag contains 7 white, 5 black and 4 red balls. Four balls are drawn without replacement. Find the probability that at least three balls are black. | 12 |

927 | The probability that ( A ) can solve a problem is ( frac{2}{3} ) and that ( B ) can solve is ( frac{3}{4} ) If both of them attempt the problem. What is probability that the problem act solved? A ( cdot frac{11}{12} ) в. ( frac{7}{12} ) c. ( frac{5}{12} ) D. ( frac{9}{12} ) | 12 |

928 | Find the probability of drawing a white ball from a box containing 3 white and 5 black balls | 12 |

929 | In a race of 12 cars, the probability that ( operatorname{car} A ) will win is ( frac{1}{5} ) and of ( operatorname{car} B ) is ( frac{1}{6} ) and that of car ( C ) is ( frac{1}{3} . ) Find the probability that only one of them won the race. | 12 |

930 | A die of six faces marked with the integers 1,2,3,4,5,6 one on each face Is thrown twice in succession what is the total number of outcomes thus obtained? | 12 |

931 | A fair coins is tossed 8 times. Find the probability that: (i) it shows no head (ii) it shows head at least once. | 12 |

932 | One mapping is selected at random from all the mappings of the set ( A= ) ( mathbf{1}, mathbf{2}, mathbf{3}, dots, boldsymbol{n} ) into itself. The probability that the mapping selected is one to one, is given by A ( cdot frac{1}{n^{n}} ) в. ( frac{1}{n !} ) c. ( frac{(n-1) !}{n^{n-1}} ) D. None of these | 12 |

933 | A dies is thrown three times and the sum of three numbers obtained is 15 The probability of first throw being 5 is: A ( cdot frac{3}{10} ) B. ( frac{2}{5} ) c. ( frac{1}{5} ) D. ( frac{4}{5} ) | 12 |

934 | A die if thrown once. Find the probability of getting a number less than 5 | 12 |

935 | Two dice are thrown simultaneously. The probability of getting a multiple of 2 on one die and a multiple of 3 on the other is A ( cdot frac{5}{36} ) в. ( frac{5}{12} ) c. ( frac{11}{36} ) D. ( frac{1}{12} ) | 12 |

936 | ( mathrm{X}^{prime} ) speaks truth in ( 60 % & ) ‘y’ is ( 50 % ) of the cases. The probability that they contradict each other while narrating the same incident, is A ( cdot frac{1}{2} ) в. ( frac{1}{8} ) ( c cdot frac{1}{4} ) D. | 12 |

937 | A die has six faces numbered from 1 to 6. It is rolled and number on the top face is noted. When this is treated as random trial. (a) What are the possible outcomes? (b) Are they equally likely? Why? (c) Find the probability of a composite number turning up on the top face. | 12 |

938 | If ( P(n) ) is the statement ” ( n^{2} ) is even”, then what is ( boldsymbol{P}(boldsymbol{3}) ) ? | 12 |

939 | A pair of unbiased dice is rolled together till a sum is either 5 or 7 is obtained, The probability that 5 comes before 7 is A . ( 2 / 5 ) в. ( 3 / 5 ) c. ( 4 / 5 ) D. none of these | 12 |

940 | ( A ) and ( B ) are events such that ( p(A cup ) ( boldsymbol{B})=mathbf{3} / mathbf{4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}(overline{boldsymbol{A}})=frac{mathbf{2}}{mathbf{3}} ) ( operatorname{then} P((bar{A} cap B) ) equals A ( cdot frac{5}{12} ) B. ( frac{3}{8} ) ( c cdot frac{4}{5} ) ( D cdot frac{5}{4} ) | 12 |

941 | The probability of drawing a red 9 from a standard pack of 52 playing cards is A ( cdot frac{1}{13} ) в. ( frac{1}{26} ) ( c cdot frac{1}{2} ) D. ( frac{1}{4} ) | 12 |

942 | If ( P(E)=0 ) then ( E ) is a/an A. sure event B. impossible event c. equally likely event D. none of these | 12 |

943 | In figure points ( A, B, C ) and ( D ) are the centre of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD.What is the probability that the point will be chosen from the shaded region? A ( cdotleft(1-frac{pi}{4}right) ) в. ( left(1-frac{pi}{2}right) ) ( c cdotleft(1-frac{pi}{6}right) ) D. ( left(2-frac{pi}{4}right) ) | 12 |

944 | For a biased die the probabilities for the different faces to turn up are given below: The die is tossed and you are told that either face one or face two turned up. Then the probability that it is face one is. Faces: Probabilities: ( quad ) 0.1 ( quad ) 0.32 ( quad ) 0.21 A. ( 1 / 6 ) в. ( 1 / 10 ) c. ( 5 / 49 ) D. ( 5 / 21 ) | 12 |

945 | The mean score of 1000 students for an examination is 34 and ( S . D . ) is 16 (i) How many candidates can be expected to obtain marks between 30 and 60 assuming the normality of the distribution and (ii) determine the limit of the marks of the central ( 70 % ) of the candidates: ( {boldsymbol{P}[mathbf{0}<boldsymbol{z}<mathbf{0 . 2 5}]=mathbf{0 . 0 9 8 7} boldsymbol{P}[mathbf{0}<boldsymbol{z}<mathbf{1} ) | 12 |

946 | 5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that all the 5 are hearts is A ( cdot frac{13}{^{52} C_{5}} ) в. c. D. ( frac{^{13} C_{5}}{^{13} C_{3} times^{13} C_{4} times^{13} C_{5}} ) | 12 |

947 | If ( Pleft(E_{k}right) propto k ) for ( 0 leq k leq n, ) the ( P(A) ) equals A. ( 3 n /(4 n+1) ) B. ( (2 n+1) / 3 n ) c. ( 1 /(n+1) ) D. ( 1 / n^{2} ) | 12 |

948 | fthe binomial distribution whose mean is 5 and variance ( frac{10}{3} ) is ( P(X=r)= ) ( ^{15} C_{r}left(frac{1}{a}right)^{r}left(frac{2}{a}right)^{15-r}, r=0,1,2, dots, 15 ) then the value of ( a ) is | 12 |

949 | Probability of an event always greater than or equal to A ( cdot frac{1}{2} ) B. 1 c. 0 D. – | 12 |

950 | There is ( 25 % ) chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days? ( ^{A} cdot_{1-}left(frac{1}{4}right)^{7} ) B. ( left(frac{1}{4}right)^{7} ) ( ^{c}left(frac{3}{4}right)^{7} ) D. ( _{1-}left(frac{3}{4}right)^{7} ) | 12 |

951 | Wher distribution of 2 black and 2 white balls in two containers are as shown.Which of the following statements is true? A. (iv) has the maximum possibility of picking a black ball B. (i) and (iv) has equal probability of picking a white ball C. (iii) has the maximum possibility of picking a white ball D. (ii) has the maximum possibility of picking a white ball | 12 |

952 | The number of ways of arranging the letters ( A A A A A, B B B, D, E E & F ) in a row if the letter ( C ) are separated from one another is ( mathbf{A} cdot_{13} s_{3} cdot frac{12 !}{5 ! 3 ! 2 !} ) в. ( frac{13 !}{5 ! 3 ! 2 !} ) c. ( frac{14 !}{3 ! 32 !} ) D. none | 12 |

953 | In a certain city two newspapers ( A ) and ( B ) are published. It is known that ( 25 % ) of the city population reads ( A ) and ( 20 % ) of the population reads ( B .8 % ) of the population reads both ( A ) and ( B ). It is known that ( 30 % ) of those who read ( A ) but not ( B ) look into advertisements and ( 40 % ) of those who read ( B ) but not ( A ) look advertisements while ( 50 % ) of those who read both ( A ) and ( B ) look into advertisements. What is the percentage of the population who reads an advertisement? A ( cdot frac{139}{500} ) в. ( frac{361}{500} ) c. ( frac{139}{1000} ) D. ( frac{861}{1000} ) | 12 |

954 | If ( x ) is a binomial variable with ( P=frac{1}{4} ) then the smallest value of ( n ) so that ( P(x geq 1)>0.70 ) is A . 3 B. 4 ( c .5 ) D. 6 | 12 |

955 | A number is selected at random from the first 1,000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or ( 11 ? ) A . 0.25 B. 0.32 c. 0.23 D. 0.33 | 12 |

956 | Two dice are thrown sumiltaneously. Find the probability that the sum of the numbers on the faces is not divisible by 4 or divisible by 5 | 12 |

957 | A card is drawn from a well shuffled pack of 52 cards. Events A and B are defined as follows: ( A: ) Getting a card of spade B : Getting an ace, then ( A ) and ( B ) are A. mutually exclusive and independent events B. not mutually exclusive but independent events c. mutually exclusive and not independent events D. neither mutually exclusive nor independent events | 12 |

958 | Assertion At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, ( 80 % ) pass the test and of the incapable, ( 25 % ) pass the test. Given that ( 40 % ) of the candidates are really capable, then the proportion of capable college students is about ( 68 % ) Reason ( Pleft(frac{A}{B}right)=frac{P(A) Pleft(frac{B}{A}right)}{P(A) Pleft(frac{B}{A}right)+Pleft(A^{prime}right) Pleft(frac{B}{A^{prime}}right)} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 12 |

959 | Tossing a coin is an example of A. space в. sample c. experiment D. event | 12 |

960 | If ( A ) and ( B ) are events such that ( P(A)= ) ( frac{3}{8}, P(B)=frac{5}{8} ) and ( P(A cup B)=frac{3}{4}, ) then ( Pleft(frac{A}{B}right)= ) ( A cdot frac{2}{3} ) B. ( frac{2}{5} ) ( c cdot frac{1}{3} ) D. | 12 |

961 | Assertion In rolling a dice, the probability of getting number 8 is zero. Reason Its an impossible event. | 12 |

962 | 9. Numbers 1 to 5 are written on separate slips, i.e one number on one slip and put in a box. Wahida pick a slip from the box without looking at it. What is the probability that the slip bears an odd number? | 11 |

963 | Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with probability ( frac{3}{4} . ) Given that the outcome is head the probability that the two-headed coin was chosen, is A. в. ( frac{2}{5} ) ( c cdot frac{1}{5} ) D. | 12 |

964 | Two cards are drawn with replacement from a well shuffled deck of 52 cards. Find the mean and variance for the number of aces | 12 |

965 | Find the number of ways in which a lady can invite 6 guests selected from 10 friends so that two of the friends will not attend the party together ?. | 12 |

966 | Which of the following is not true? A ( cdot P_{700}>2 / 3 ) В. ( P_{101}2 / 3 ) D. none of these | 12 |

967 | The probability that it will rain on a particular day is 0.64 what is the probability that it will not rain on that day? | 12 |

968 | Find the probability of scoring a total of more than ( 7, ) when two dice are thrown A ( .5 / 12 ) B. ( 5 / 18 ) ( c .5 / 6 ) D. ( 5 / 24 ) | 12 |

969 | (i) ( A ) lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? (ii) Suppose the bulb drawn in (i) is not defective and not replaced. Now bulb is drawn at random from the rest. What is the probability that thisbulb is not defective? | 12 |

970 | If ( A, B ) and ( C ) are three events such that ( boldsymbol{P}(boldsymbol{B})=frac{1}{2} ; boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}^{prime}right)=frac{1}{3} ) and ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B} cap boldsymbol{C}^{prime}right)=frac{1}{336} operatorname{then} boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is equal to ( dots ) A ( cdot frac{328}{2016} ) в. ( frac{330}{2016} ) c. ( frac{324}{2016} ) D. ( frac{320}{2016} ) | 12 |

971 | The distance (in ( mathrm{km} ) ) of 40 engineers from their residence to their place of work were found as follows: [ begin{array}{ccccccccc} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 \ 19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 \ 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 end{array} ] ( begin{array}{llllll}mathbf{1 2} & mathbf{1 4} & mathbf{2} & mathbf{9} & mathbf{6} & mathbf{1 5}end{array} ) 15 [ 7 ] What is the empirical probability that an engineer lives: (i) less than ( 7 k m ) from her place of work? (ii) more than or equal to ( 7 k m ) from her place of work? (iii) within ( frac{1}{2} k m ) from her place of work? | 12 |

972 | If ( A ) and ( B ) are two events such that ( P(A)=frac{3}{8}, P(B)=frac{5}{8} ) and ( P(A cup B)=frac{3}{4}, ) then ( P(A cap bar{B})= ) ( A cdot frac{5}{8} ) B. ( frac{3}{8} ) ( c cdot frac{1}{8} ) D. | 12 |

973 | There are 15 tickets in a box, each bearing one of the numbers from 1 to 15 One ticket is drawn from the box. Find the probability of event that the ticket drawn – (1) shows an even number. (2) shows a number which is a multiple of 5. | 12 |

974 | A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn at random. The probability that they are not of same colour is ( ^{mathrm{A}} cdot frac{37}{44} ) в. ( frac{31}{44} ) c. ( frac{21}{44} ) D. ( frac{41}{44} ) | 12 |

975 | Let ( X ) be a random variable which assumes values ( x_{1}, x_{2}, x_{3}, x_{4} ) such that ( mathbf{2} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{1}right)=mathbf{3} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{2}right)=boldsymbol{P}(boldsymbol{X}= ) ( left.boldsymbol{x}_{3}right)=mathbf{5} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{4}right) ) Find the probability distribution of ( boldsymbol{X} ) | 12 |

976 | How many five letters words can be formed using the letter ( boldsymbol{T} boldsymbol{I} ) MRET? | 12 |

977 | Two coins are tossed. Find the conditional probability that two Heads will occur given that at least one occurs A ( cdot frac{1}{3} ) B. ( frac{1}{2} ) ( c cdot frac{1}{4} ) D. none of these | 12 |

978 | A natural number ( x ) is chosen at random from the first 120 natural numbers and it is observed to be divisible by 8 , then the probability that it is not divisible by 6 is ( A cdot frac{1}{3} ) B. ( c cdot frac{3}{4} ) D. ( frac{2}{3} ) | 12 |

979 | If ( A ) and ( B ) are independent events with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5 .} ) then find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) | 12 |

980 | Let ( X ) and ( Y ) be two events such that ( P(X)=frac{1}{3}, P(X / Y)=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{Y} / boldsymbol{X})=frac{2}{5} cdot ) Then This question has multiple correct options ( ^{mathbf{A}} cdot P(X cup Y)=frac{2}{5} ) В ( cdot P(Y)=frac{4}{15} ) ( c cdot Pleft(X^{prime} mid Yright)=frac{1}{2} ) D. ( P(X cap Y)=frac{1}{5} ) | 12 |

981 | Let ( S_{n}=sum_{k=1}^{n} k ) denote the sum of the first ( n ) positive integers. The numbers ( boldsymbol{S}_{1}, boldsymbol{S}_{2}, boldsymbol{S}_{3}, ldots, boldsymbol{S}_{99} ) are written on ( boldsymbol{9 9} ) cards. The probability of drawing a card with an even number written on it is A ( cdot frac{1}{2} ) в. ( frac{49}{100} ) c. ( frac{49}{99} ) D. ( frac{48}{99} ) | 12 |

982 | toppr LoGin Q Type your question to Rs. ( 50,000 . ) The data about the number of persons in various categories is as under: Monthly ( quad ) Number of Cars income | 12 |

983 | The probability that at least one of the events ( A ) and ( B ) occurs is ( frac{3}{5} . ) If ( A ) and ( B ) occur simultaneously with probability ( frac{1}{5} operatorname{then} Pleft(A^{prime}right)+Pleft(B^{prime}right) ) is A ( cdot frac{2}{5} ) B. ( frac{4}{5} ) ( c cdot frac{6}{5} ) D. | 12 |

984 | Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10 . The probability that both will quailfy the examination is 0.02 . Find the probability that (a) Both Anil and Ashima will not qualify the examination. (N) (b) Atleast one of them will not qualify the examination. (N) (c) Only one of them will qualify the examination. (N) | 12 |

985 | There are two urns. There are ( m ) white ( & ) ( boldsymbol{n} ) black balls in the first urn and ( boldsymbol{p} ) white & ( q ) black balls in the second urn. One ball is taken from the first urn & placed into the second. Now, the probability of drawing a white ball from the second urn is A ( cdot frac{p m+(p+1) n}{(m+n)(p+q+1)} ) B. ( frac{(p+1) m+p n}{(m+n)(p+q+1)} ) c. ( frac{q m+(q+1) n}{(m+n)(p+q+1)} ) D. ( frac{(q+1) m+q n}{(m+n)(p+q+1)} ) | 12 |

986 | If ( A & B ) are two events such that ( P(B) neq 1, B^{C} ) denotes the event complementary to B, then This question has multiple correct options ( ^{mathbf{A}} cdot Pleft(A / B^{C}right)=frac{P(A)-P(A cap B)}{1-P(B)} ) B . ( P(A cap B) geq P(A)+P(B)-1 ) C . ( P(A)> <P(A) ) | 12 |

987 | 26. Let A and B be two events such that P(AUB) 6′ P(ANB) = 2 and P(A) = 4, where A stands for the complement of the event A. Then the events A and B are (JEEM 2014] (a) independent but not equally likely. (6) independent and equally likely. (c) mutually exclusive and independent. (d) equally likely but not independent. | 12 |

988 | Two persons appear for an interview.Probability of their selection ( operatorname{are} frac{1}{4} ) and ( frac{1}{6} ) respectively. Find the probability that none of them gets selected. | 12 |

989 | The probability distribution of a random variable is given below: [ begin{array}{llll} boldsymbol{X}=boldsymbol{x} & 0 & 1 & 2 \ P(X= & 0 & K & 2 K end{array} ] ( 2 k quad 3 K ) [ x) ] [ text { Then } boldsymbol{P}(mathbf{0}<boldsymbol{X}<mathbf{5})= ] A ( cdot frac{1}{10} ) B. ( frac{3}{10} ) ( c cdot frac{8}{10} ) D. ( frac{7}{10} ) | 12 |

990 | Two mutually exclusive events are always independent always. A. True B. False | 12 |

991 | A coin is tossed 40 times and it showed tail 24 times.The probability of getting a head was: A ( cdot frac{2}{5} ) B. ( frac{3}{5} ) ( c cdot frac{1}{2} ) D. ( frac{17}{40} ) | 12 |

992 | 1 P lus. 7. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is: (i) black (ii)red (iii) not green | 11 |

993 | ( boldsymbol{P}(boldsymbol{A})=frac{1}{boldsymbol{Z}} ) ( boldsymbol{P}(boldsymbol{B})=frac{1}{boldsymbol{4}} ) ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{1}{mathbf{5}} ) ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=? ) | 12 |

994 | Assume that a factory has two machines ( A ) and ( B ). Past records shows that machine ( A ) produces ( 60 % ) of the items of output and machine ( boldsymbol{B} ) produces ( 40 % ) of the items. Further, ( 2 % ) of the items produced by machine ( boldsymbol{A} ) were defective and only ( 1 % ) produced by machine ( B ) were defective. If a detective item is drawn at random, what is the probability that it was produced by machine ( boldsymbol{A} ) ? | 12 |

995 | ‘X’ speaks truth in ( 60 % ) of the cases and ‘Y’ in ( 50 % ) of the cases. The probability that they contradict each other while narrating the some incident, is A ( cdot frac{1}{2} ) B. ( frac{3}{4} ) ( c cdot frac{3}{5} ) D. None of these | 12 |

996 | The score of the player placing II was A ( cdot 5 frac{1}{2} ) в. ( 6 frac{1}{2} ) ( c cdot 6 ) D. ( operatorname{can}^{prime} t ) say | 12 |

997 | toppr Q Type your question ( A_{1}= ) last digit of the product is not the number 1,3,7 or 9 ( A_{2}= ) last digit of the product is among the number 1,3,5,7 or 9 ( A_{3}= ) last digit of the product is among the number 1,3,7 or 9 ( A_{4}= ) last digit of Ihe product ‘is among the number 2,4,6 or 8 ( A_{5}= ) last digit of the product is the number 5. ( A_{6}= ) last digit of the product is the number 0 ( A_{7}= ) last digit of the product is 1,2,3,4,6,7,8 or ( 9.0 n ) the basis of above information answer the following questions. The chance that last digit of the product is ( boldsymbol{A}_{3} ) ( ^{mathrm{A}} cdotleft(frac{3}{5}right)^{prime} ) B. ( left(frac{2}{5}right)^{n} ) ( ^{c} cdotleft(frac{2}{3}right)^{n} ) D. ( left(frac{4}{5}right)^{prime} ) | 12 |

998 | If ( P(E) ) denotes the probability of an event ( mathrm{E} ), then A. ( P(E)1 ) c. ( 0 leq P(E) leq 1 ) D. ( -1 leq P(E) leq 1 ) | 12 |

999 | The probability of an event which is sure to occur at every performance of an experiment is called a A. simple event B. compound event c. complementary event D. certain event | 12 |

1000 | A family has three children. Event ( A ) is that family has at most one boy, Event ( B^{prime} ) is that family has at least one boy and one girl, Event ( ^{prime} C^{prime} ) is that the family has at most one girl. Find whether events ( ^{prime} A^{prime} ) and ( ^{prime} B^{prime} ) are independent. Also find whether ( A, B, C ) are independent or not | 12 |

1001 | A coin is tossed 150 times and the outcomes are recorded. The frequency distribution of the outcomes ( H ) (i.e., head) and ( T ) (i.e., tail) is given below : Outcome [ begin{array}{ll} boldsymbol{H} & boldsymbol{T} \ & \ 85 & 65 end{array} ] Frequency Find the value of ( P(H) ), i.e., probability of getting a head in a single trial. ( mathbf{A} cdot P(H)=0.769(text { approx }) ) B . ( P(H)=0.663 ) (approx) ( mathbf{c} cdot P(H)=0.567(text { approx }) ) D. None of these | 12 |

1002 | The probability that ( A ) hits a target is ( frac{1}{3} ) and the probability that ( B ) hits it, is ( frac{2}{5} ) What is the probability that the target will be hit, if each one of ( A ) and ( B ) shoots at the target? | 12 |

1003 | A bag contains four tickets marked with ( 112,121,211,222, ) one ticket is drawn at random from the bag. Let ( boldsymbol{E}_{i}(boldsymbol{i}=mathbf{1}, mathbf{2}, mathbf{3}) ) denote the event that ( boldsymbol{i}^{t h} ) digit on the ticket is 2 then : This question has multiple correct options A ( . E_{1} ) and ( E_{2} ) are independent B. ( E_{2} ) and ( E_{3} ) are independent C ( . E_{3} ) and ( E_{1} ) are independent D. ( E_{1}, E_{2}, E_{2} ) are independent | 12 |

1004 | A fair coin is tossed five times. If the out comes are 2 heads and 3 tails (in some order), then what is the probability that the fourth toss is a head? A ( cdot frac{1}{4} ) B. ( frac{2}{5} ) ( c cdot frac{1}{2} ) D. ( frac{3}{5} ) | 12 |

1005 | Which of the following are equally likely outcomes? A. Tossing a coin getting head or tail B. While throwing a die getting any one of 6 numbers c. Both A and B D. None of these | 12 |

1006 | Suppose Mr. Ramesh have rupee 2,3 and 5 notes. In howmany ways he can get a sum of rupees 83 such that atleast one note of each type is present and the number of 2 rupee note(s) is less than number of 3 rupee note(s) which is again less than the number of 5 rupees note ( (s) ) A . 8 B. 9 c. 10 D. 12 | 12 |

1007 | A fair coin is tossed 100 times. The probability of getting tails an odd number of times is A ( cdot frac{1}{2} ) B. ( frac{1}{4} ) c. ( frac{1}{8} ) D. ( frac{3}{8} ) | 12 |

1008 | The number of ways in which 10 candidates ( A_{1}, A_{2}, dots, A_{10} ) can be ranked so that ( A_{1} ) is always above ( A_{2} ) is:- A ( cdot frac{10 !}{2} ) B . ( 2^{7} 3^{4} 5^{2} 7^{1} ) ( mathbf{c} cdot 2^{8} 5^{2} ) D. ( 3^{4} 5^{2} 7 ) | 12 |

1009 | If two events ( A ) and ( B ) such that ( Pleft(A^{c}right) ) ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}left(boldsymbol{A B}^{c}right)=mathbf{0 . 5}, ) then ( boldsymbol{P}left[boldsymbol{B} /left(boldsymbol{A} cup boldsymbol{B}^{c}right)right]= ) A . 0.25 B. 0.50 c. 0.75 D. None of these | 12 |

1010 | For the numbers in the list, write down (a) the range (b) the mode (c) the median | 12 |

1011 | If ( X ) is normally distributed with mean 6 and standard deviation ( 5, ) find: (i) ( boldsymbol{P}[mathbf{0} leq boldsymbol{X} leq mathbf{8}] ) (ii) ( boldsymbol{P}(|boldsymbol{X}-mathbf{6}|<mathbf{1 0}) ) Here ( boldsymbol{P}(mathbf{0}<boldsymbol{Z}<mathbf{1} . mathbf{2})=mathbf{0 . 3 8 4 9} ) ( boldsymbol{P}(mathbf{0}<Z<mathbf{0 . 4})=mathbf{0 . 1 5 5 4} ) ( boldsymbol{P}(mathbf{0}<boldsymbol{Z}<mathbf{2})=mathbf{0 . 4 7 7 2} ) | 12 |

1012 | State and prove Bayes’ theorem | 12 |

1013 | It has been found that if ( A ) and ( B ) play a game 12 times, ( A ) wins 6 times, ( B ) wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternately, is : A ( cdot frac{5}{12} ) в. ( frac{5}{36} ) c. ( frac{19}{27} ) D. ( frac{5}{27} ) | 12 |

1014 | A die is thrown. Write the sample space. If ( B ) is the event of getting an even number, write the event ( B ) using set notation. | 12 |

1015 | In a simultaneous throw of a pair of dice, if the probability of getting a sum less then 6 is ( frac{5}{a} . ) Find ( a ) | 12 |

1016 | A ball is drawn at random from box ( boldsymbol{I} ) and transferred to box ( I I ). If the probability of drawing a red ball from box ( I, ) after this transfer, is ( frac{1}{3}, ) then the correct option(s) with the possible values of ( n_{1} ) and ( n_{2} ) is (are) This question has multiple correct options A ( cdot n_{1}=4 ) and ( n_{2}=6 ) B . ( n_{1}=2 ) and ( n_{2}=3 ) c. ( n_{1}=10 ) and ( n_{2}=20 ) D. ( n_{1}=3 ) and ( n_{2}=6 ) | 12 |

1017 | A bag contains 10 white, 5 black, 3 green and 2 red balls. One ball is drawn at random. Find the probability that the ball drawn is white or black or green | 12 |

1018 | The probability that a marksman will hit a target is given as ( frac{1}{5}, ) then his probability of at least one hit in 10 shots is ( ^{mathrm{A}} cdot_{1}-left(frac{4}{5}right)^{10} ) в. ( frac{1}{510} ) c. ( _{1-frac{1}{5^{10}}} ) D. None of these | 12 |

1019 | 1500 families with 2 children were selected randomly, and the following data were recorded: No. of girls in family No. of families | 12 |

1020 | If ( A ) and ( B ) are two mutually exclusive events in a sample space ( S ) such that ( boldsymbol{P}(boldsymbol{B})=2 boldsymbol{P}(boldsymbol{A}) ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{S} ) then ( boldsymbol{P}(boldsymbol{A})= ) A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{4} ) D. | 12 |

1021 | What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin? A . 6 B. 7 c. 8 D. None of the above | 12 |

1022 | Tell whether the following is certain to happen, possible can happen but not certain Tomorrow will be a cloudy day. | 12 |

1023 | In a school, there are 1000 student, out of which 430 are girls. It is known that out of ( 430,10 % ) of the girls study in class ( X I I . ) What is the probability that a student chosen randomly studies in class ( X I I ) given that the chosen student is a girl?. | 12 |

1024 | Three dice are rolled. The probability that the same number will appear on each of them is A ( cdot frac{1}{36} ) B. ( frac{1}{12} ) c. ( frac{2}{49} ) D. None | 12 |

1025 | Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl? A. 0.33,0.34 В. 0.88,0.98 c. 0.78,0.67 D. 0.5,0.33 | 12 |

1026 | The variable which takes some specific values is called A. discrete random variable B. continuous random variable c. both A and B D. none | 12 |

1027 | A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows: ( begin{array}{cccccc}0.03 & 0.08 & 0.08 & 0.09 & 0.04 & 0.17 \ 0.16 & 0.05 & 0.02 & 0.06 & 0.18 & 0.20 \ 0.11 & 0.08 & 0.12 & 0.13 & 0.22 & 0.07 \ 0.08 & 0.01 & 0.10 & 0.06 & 0.09 & 0.18 \ 0.11 & 0.07 & 0.05 & 0.07 & 0.01 & 0.04end{array} ) Using this table, find the probability of the concentration of sulphur dioxide in the interval ( 0.12-0.16 ) on any of these days. | 12 |

1028 | In an entrance test is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7 . The probability of passing at least of them is ( 0.95 . ) What is the probability of passing both? | 12 |

1029 | One number is to be chosen from Numbers 1 to ( 100, ) the probability that it is divisible by 3 or 7 is….. A ( frac{33}{100} ) в. ( frac{7}{100} ) c. ( frac{4}{100} ) D. ( frac{43}{100} ) | 12 |

1030 | Two coins are tossed once, where (i) ( E: ) tail appears on one coin, ( boldsymbol{F}: ) one coin shows head (ii) ( E: ) no tail appears, ( boldsymbol{F}: ) no head appears Determine ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) ) A .1,0 в. 1,0.2 c. 0,2 D. 1,3 | 12 |

1031 | The probability of event is 0 A. Sure B. Impossible c. Exclusive D. None of these | 12 |

1032 | An artillery target may be either at point ( I ) with probability ( frac{8}{9} ) or at point ( I I ) with probability ( frac{1}{9} . ) We have 21 shells each of which can be fired at point ( I ) or ( I I ). Each shell may hit the target independently of the other shell with probability ( frac{1}{2} . ) How many shells must be fired at point ( I ) to hit the target with maximum probability? A. ( P(A) ) is maximum where ( x=11 ). B. ( P(A) ) is maximum where ( x=12 ) c. ( P(A) ) is maximum where ( x=14 ) D. ( P(A) ) is maximum where ( x=15 ) | 12 |

1033 | The outcome of each of 30 items was observed; 10 items gave an outcome ( frac{1}{2} ) deach, 10 items gave outcome ( frac{1}{2} ) each and the remaining 10 items gave outcome ( frac{1}{2}+d ) each. If the variance of this outcome data is ( frac{4}{3} ) then ( |boldsymbol{d}| ) equals:- A. 2 B. ( frac{sqrt{5}}{2} ) ( c cdot frac{2}{3} ) D. ( sqrt{2} ) | 12 |

1034 | If ( A ) and ( B ) are mutually exclusive such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

1035 | Which one of the following cannot be the probability of an event. A ( cdot frac{1}{3} ) в. ( frac{11}{36} ) c. ( -frac{2}{3} ) ( D ) | 12 |

1036 | Six boys and girls sit in a row randomly Find the probability that the six girls sit together. A ( cdot p=frac{1}{95040} ) B. ( _{p}=frac{1}{132} ) c. ( _{p}=frac{1}{924} ) D. ( p=frac{1}{66} ) | 12 |

1037 | A coin is tossed 3 times. The probability of getting head and tail alternately is A ( cdot frac{1}{8} ) B. ( frac{1}{2} ) ( c cdot frac{1}{4} ) D. | 12 |

1038 | ( A ) and ( B ) are events with ( P(A)= ) ( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3} ) Find the probability that neither ( A ) and ( B ) occurs. | 12 |

1039 | A card is thrown from a pack of 52 cards so that each card equally likely to be selected. Then find whether the events ( A ) and ( B ) independent? ( A= ) the card drawn is spade, ( B= ) the card drawn in an ace. | 12 |

1040 | Three persons ( A, B ) and ( C ) apply for a job of Manager in a Private company. Chance of their selection ( (A, B text { and } C) ) are in the ratio ( 1: 2: 4 . ) The probability that ( A, B ) and ( C ) can introduce changes to improve profits of company are 0.8,0.5 and 0.3 respectively, if the changes does not take place, find the probability that it is due to the appointment of ( boldsymbol{C} ) | 12 |

1041 | One hundred identical coins, each with probability ( p ) of showing heads are tossed once. If ( 0<p<1 ) and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of ( p ) is A ( cdot 1 / 2 ) B. ( 51 / 101 ) c. ( 49 / 101 ) D. 3 / 101 | 12 |

1042 | The mean and variance of a binomial distribution are 4 and 3 respectively. Fix the distribution and find ( P(X geq 1) ) | 12 |

1043 | In a shooting game, John shoots the balls 20 times out of 40 trials. What is the empirical probability of the shooting event? A ( cdot frac{3}{2} ) в. ( frac{1}{2} ) ( c cdot frac{5}{2} ) D. ( frac{7}{2} ) | 12 |

1044 | If ( A ) is an event of a random experiment such that ( P(A): P(bar{A})=5: 11 ), then find ( P(A) ) and ( P(bar{A}) ) | 12 |

1045 | ( A ) is known to tell the truth in 5 cases out of 6 and he states that a white ball was drawn from a bag containing 8 black and 1 white ball. The probability that the white ball was drawn, is A ( cdot frac{7}{13} ) B. ( frac{5}{13} ) ( c cdot frac{9}{13} ) D. None of these | 12 |

1046 | The probability of getting a boy in a class is 0.6 and there are 45 students In a class, then find the number of girls in the class. | 12 |

1047 | A player tosses two fair coins. He wins Rs. ( 5 /- ) if two heads occur, ( R s .2 /- ) if one head occurs and ( R s .1 /- ) if no head occurs. Then his expected gain is A ( cdot ) Rs. ( frac{8}{3} ) в. ( operatorname{Rs} . frac{7}{3} ) c. ( R s .2 .5 ) D. Rs.1.5 | 12 |

1048 | A letter is known to have come eithe from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from London? A ( cdot frac{12}{17} ) в. ( frac{5}{17} ) c. ( frac{5}{12} ) D. ( frac{7}{12} ) | 12 |

1049 | A fair die is tossed. If 2,3 or 5 occurs, the player wins that number of rupees, but if 1,4 or 6 occurs, the player loses that number of rupees. Then find the possible payoffs for the player. | 12 |

1050 | The probability of an impossible event is A . B. 0 c. less than 0 D. greater than 1 | 12 |

1051 | What is the total number of elementary events associated to the random experiment of throwing three dice together | 12 |

1052 | A coin is tossed ( (mathbf{m}+mathbf{n}) ) times ( (mathbf{m}<mathbf{n}) ) The probability for getting atleast 'n consecutive heads is A ( cdot frac{m+2}{2^{n+1}} ) в. ( frac{n+2}{2^{m+1}} ) c. ( frac{m}{2^{n+1}} ) D. ( frac{(m+1) times(m+2)}{2^{(m+n+1)}} ) | 12 |

1053 | Let ( A ) and ( B ) be independent events with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=0.5 . ) Then find: (i) ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) ) (ii) ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A}) ) ( (text { iii) } boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) (iv) ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

1054 | Assuming the balls to be identical except for difference in colors, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is A. 880 в. 629 ( c .630 ) D. 879 | 12 |

1055 | Consider the following statements: 1. If ( A ) and ( B ) are exhaustive events, then their union is the sample space. 2. If ( A ) and ( B ) are exhaustive events, then their intersection must be an empty event. Which of the above statements is/are correct? A. 1 only B. 2 only c. Both 1 and 2 D. Neither 1 nor 2 | 12 |

1056 | The chance that a person with two dices, the faces of each being numbered 1 to ( 6, ) will throw aces exactly 4 times in 6 trials is ( ^{mathrm{A}} cdotleft(frac{1}{36}right)^{4} ) ( ^{mathrm{B}}left(frac{1}{36}right)^{4}left(frac{35}{36}right)^{2} ) ( ^{mathbf{c}} cdot_{4} Cleft(frac{1}{36}right)^{4}left(frac{35}{36}right)^{2} ) ( ^{mathrm{D}} cdot_{4}^{6} Cleft(frac{1}{36}right)^{2}left(frac{35}{36}right)^{4} ) | 12 |

1057 | If ( boldsymbol{E} ) and ( boldsymbol{F} ) be events in a sample space such that ( boldsymbol{P}(boldsymbol{E} cup boldsymbol{F})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})= ) 0.3 and ( P(E)=0.5, ) then ( P(F) ) is A . 0.6 B. ( c .0 .8 ) D. None | 12 |

1058 | If ( A ) and ( B ) are mutually exclusive such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

1059 | The probabilities of three events ( A, B & ) ( C operatorname{are} P(A)=0.6, P(B)=0.4 ) and ( P(C)=0.5 ) If ( P(A cup B)=0.8, P(A cap C)=0.3, P(A cap ) ( B cap C)=0.2 & P(A cup B cup C) geq 0.85 ) Find the range of ( mathrm{P}(B cap C) ) B . [0.25,0.35] c. [0.2,0.3] D. [0.2,0.4] | 12 |

1060 | A die is thrown. If ( A ) is the event that the number on upper face is less than 5 then write sample space and event ( A ) in set notation. | 12 |

1061 | An ordinary pack of 52 cards is well shuffled. The top card is then turned over. What is the probability that the top card is a king card. | 12 |

1062 | There are 5 percent defective items in a large bulk of items. The probability that a sample of 10 items will include not more than one defective item is ( left(frac{19^{9} times 29}{20^{x}}right), ) then what is the value of ( boldsymbol{x} ) | 12 |

1063 | An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of same colour. The process is repeated. The probability that the third ball drawn is black is1 ( -frac{k}{30} ). Find the value of ( k ) ? | 12 |

1064 | If ( A ) and ( B ) are independent events of ( a ) random experiment such that ( boldsymbol{P}(boldsymbol{A} cap ) ( B)=frac{1}{6} ) and ( P(bar{A} cap bar{B})=frac{1}{3}, ) then ( P(A) ) is equal to A ( cdot frac{1}{3} ) B. ( frac{2}{3} ) ( c cdot frac{5}{7} ) D. None of these | 12 |

1065 | The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months. A . 0.2316 B. 0.0062 c. 0.0072 D. 0.2136 | 12 |

1066 | A card is drawn from a pack of 52 cards. The probability of getting a queen of spade or a king of diamond is A ( cdot frac{1}{56} ) в. ( frac{1}{26} ) c. ( frac{1}{52} ) D. ( frac{3}{56} ) | 12 |

1067 | The probability of the simultaneous occurrence of two events ( A ) and ( B ) is ( p ). If the probability that exactly one of ( A, B ) occurs is ( boldsymbol{q} ), then This question has multiple correct options A ( cdot Pleft(A^{prime}right)+Pleft(B^{prime}right)=2+2 q-p ) B . ( Pleft(A^{prime}right)+Pleft(B^{prime}right)=2-2 p-q ) c. ( P(A cap B mid A cup B)=frac{p}{p+q} ) D . ( Pleft(A^{prime} cap B^{prime}right)=1-p-q ) | 12 |

1068 | An unbiased die is thrown again and again until three sixes are obtained. The probability of obtaining ( 3 mathrm{rd} ) six in the sixth throw of the die is ( frac{1250}{x^{x}} ) | 12 |

1069 | If ( mathrm{E} & mathrm{F} ) are events with ( boldsymbol{P}(boldsymbol{E}) leq boldsymbol{P}(boldsymbol{F}) & ) ( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})>0, ) then? A. Occurrence of ( E Rightarrow ) occurrence of ( F ) B. Occurrence of F ( Rightarrow ) occurrence of E c. Non-occurrence of ( E Rightarrow ) non-occurrence of ( F ) D. None of the above implications holds | 12 |

1070 | Two unbiased dice are thrown. The probability that the sum of the numbers appearing on the top face of two dice is greater than 7 if 4 appear on the top face of the first dice is… A ( cdot frac{1}{3} ) B. ( frac{1}{2} ) c. ( frac{1}{12} ) D. | 12 |

1071 | 8. A glass jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Hari takes out a marble from the jar at random. What is the probability that the chosen marble is of red colour? | 11 |

1072 | Mixed/Compound/Composite event | 12 |

1073 | Assertion If ( A & B ) are two events such that ( P(A)=frac{2}{5}, P(B)=frac{3}{4} ) then ( frac{1}{20} leq ) ( P(A cap B) leq frac{2}{5} ) Reason ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) leq max {boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(B)} & ) ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) geq min {boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(boldsymbol{B})} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

1074 | Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is? A . ( 1 / 6 ) B . ( 1 / 36 ) c. ( 12 / 151 ) D. None of these | 12 |

1075 | A bag contains cards numbered from 1 to ( 49 . ) A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is (i) an odd number (ii) a multiple of 5 (iii) a perfect square (iv) an even prime number | 12 |

1076 | Two squares are chosen from the squares of an ordinary chess board. It is given that the selected squares do not belong to the same row or column. The probability that they have a side in common A ( cdot frac{25}{49} ) в. ( frac{32}{49} ) c. ( frac{1}{18} ) D. | 12 |

1077 | If two events ( A ) and ( B ) are such that ( boldsymbol{P}left(boldsymbol{A}^{prime}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right)=mathbf{0 . 5}, operatorname{then} boldsymbol{P}left(frac{boldsymbol{B}}{boldsymbol{A} cup boldsymbol{B}^{prime}}right) ) equala A ( cdot frac{3}{4} ) B. ( c cdot frac{1}{4} ) D. | 12 |

1078 | If ( P(A)=1, ) then the event ( A ) is known as A. Symmetric event B. Dependent event c. Improbable event D. Sure event | 12 |

1079 | A die is thrown 100 times with frequency for the outcomes 1,2,3,4,5 and 6 as given this following table Find the probability of getting Number greater than 5 as an outcome. | 12 |

1080 | The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is A . 40 B. 60 c. 80 D. 100 | 12 |

1081 | Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red. | 12 |

1082 | There are 2 brothers ( A ) and B. Probability that ( A ) will pass in exam is ( 3 / 5 ) and that B will pass in exam is ( 5 / 8 . ) What will be the probability that only one will pass in the exam? | 12 |

1083 | The probability’p’ of happening of an event A. Can be negative В. ( 0 leq p leq 1 ) c. can be greater the 1 D. None of these | 12 |

1084 | Three coins are tossed. Describe two events ( A ) and ( B ) which are mutually exclusive. | 12 |

1085 | If two events ( A ) and ( B ) are such that ( P(A)>0 ) and ( P(B)=1, ) then ( P ) is equal to A ( cdot_{1-P}left(frac{A}{B}right) ) в. ( _{1-P}left(frac{A^{prime}}{B}right) ) ( ^{c} cdot_{1-P}left(frac{A cup B}{B^{prime}}right) ) D. ( Pleft(frac{A}{B^{prime}}right) ) | 12 |

1086 | Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or ( 5 ? ) A ( cdot frac{7}{20} ) в. ( frac{8}{20} ) c. ( frac{6}{20} ) D. ( frac{9}{20} ) | 12 |

1087 | ( A ) and ( B ) are two candidates seeking admission in I.I.T. The probability that ( boldsymbol{A} ) is selected is 0.5 and the probability that both ( A ) and ( B ) are selected is atmost ( 0.3 . ) Is it possible that the probability of ( boldsymbol{B} ) getting selected is ( mathbf{0 . 9} ) ? If it is possible then enter 1 , else enter 0 | 12 |

1088 | If ( E_{1} ) and ( E_{2} ) are two events such that ( boldsymbol{P}left(boldsymbol{E}_{1}right)=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}left(boldsymbol{E}_{2}right)=frac{mathbf{1}}{mathbf{2}} ; boldsymbol{P}left(frac{boldsymbol{E}_{1}}{boldsymbol{E}_{2}}right)=frac{mathbf{1}}{mathbf{4}} ) then choose the correct options. A. ( E_{1} ) and ( E_{2} ) are mutually exclusive B. ( E_{1} & E_{2} ) are dependent c. ( E_{1} ) and ( E_{2} ) are independent D. ( E_{1} ) and ( E_{2} ) are exhaustive | 12 |

1089 | A number is chosen at random among the first 120 natural numbers, The probability of the number chosen being a multiple of 5 or 15 is A . ( 1 / 5 ) в. 1 18 c. ( 1 / 6 ) D. none of these | 12 |

1090 | In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to: A ( cdot frac{150}{6^{5}} ) в. ( frac{175}{6^{5}} ) c. ( frac{200}{6^{5}} ) D. ( frac{225}{6^{5}} ) | 12 |

1091 | A bag contains four tickets numbered ( 00,01,10,11 . ) Four tickets are chosen at random with replacement, the probability that the sum of the numbers on the tickets is ( 23, ) is A ( .3 / 32 ) в. ( 1 / 64 ) c. ( 5 / 256 ) D. ( 7 / 256 ) | 12 |

1092 | A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than ( 9, ) given that the black die resulted in a 5 . (b) Find the conditional probability of obtaining the sum 8 , given that the red die resulted in a number less than 4 A. 0.33,0.11 B. 0.51,0.76 c. 0.56,0.43 D. 0.11,0.65 | 12 |

1093 | Find the number of ways in which 5 boys and 5 girls be seated in a row so that no two girls may sit together. | 12 |

1094 | If ( boldsymbol{P}(boldsymbol{E})=mathbf{0 . 8 7}, ) find ( boldsymbol{P}(overline{boldsymbol{E}}) ) | 12 |

1095 | Assertion If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) cdot mathbf{A}, mathrm{B} ) are two non mutually exclusive events then ( boldsymbol{P}(boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) ) Reason For non mutually exclusive events ( (A cap B) neq phi ) and ( P(A / B)= ) ( frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{B})}, boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{A})} ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

1096 | A die is thrown 24 times. If number 4 come up 12 times, the probability of number 4′ is The followine data th K . Then the value of k is e m to the model of 2 | 10 |

1097 | From a well shuffied pack of cards one card is drawn at random. The probability that the card drawn is an ace is A ( cdot frac{1}{13} ) в. ( frac{1}{14} ) c. ( frac{3}{52} ) D. ( frac{1}{26} ) | 12 |

1098 | A throws a coin 3 times. If he get a head all three times, he is to get a reward of Rs.200, on the other hand if he does not get 3 heads he is to loose Rs.40. He is expected to win Rs. A . Rs. 50 B. Rs. (-10) c. Rs. 35 D. Rs. 10 | 12 |

1099 | Probability cannot be expressed in A. fraction form B. ratio form c. negative form D. percentage form | 12 |

1100 | A man is known to speak the truths 3 out of 4 times. He throw a die and report that it is six. The probability that it is actually a six, is A ( cdot frac{3}{8} ) B. ( frac{1}{5} ) ( c cdot frac{3}{4} ) D. None of these | 12 |

1101 | A couple has two children, (i) Find the probability that both children are males, if it is known that at least one of the children is male. (ii) Find the probability that both children are females, if ti is known that the elder child is a female. A. 0.55,0.38 В. 0.33,0.50 c. 0.67,0.78 D. 0.56,0.67 | 12 |

1102 | In a group of 10 people, ( 70 % ) take vitamins. If you randomly choose 2 of them, what is the probability that neither person selected takes vitamins? A ( . . .0677 ) в ( ldots .09 ) ( c ldots 30 ) D ( ldots 4 ) ( E ldots .49 ) | 12 |

1103 | There are three boxes, each containing a different number of light bulbs. The first box has 10 bulbs, of which four are dead, the second has six bulbs, of which one is dead, and the third box has eight bulbs of which three are dead. What is the probability of a dead bulb being selected when a bulb is chosen at random from one of the three boxes? A. ( frac{115}{330} ) В. ( frac{113}{360} ) c. ( frac{113}{330} ) D. None of these | 12 |

1104 | (a) T6 16 32 16 . A bag contains 4 red and 6 black balls. A ball is de random from the bag, its colour is observed and th: along with two additional balls of the same colour a turned to the bag. If now a ball is drawn at random fro bag, then the probability that this drawn ball is red all is drawna and this ball colour are re- [JEEM 2018 (a) 2 (b) – 2 (c) (d) To are raun successively with replacement from | 12 |

1105 | If ( A ) and ( B ) are two event such that ( P(A)=frac{6}{11}, P(B)=frac{5}{11} ) and ( P(A cup ) ( B)=frac{7}{11}, ) find ( P(A r ) ( boldsymbol{B}), boldsymbol{P}(boldsymbol{A} / boldsymbol{B}), boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) ) | 12 |

1106 | If ( A, B ) and ( C ) are three events, then This question has multiple correct options A ( . P(text { exactly two of } A, B, C text { occur }) leq P(A cap B)+P(B cap ) ( C)+P(C cap A) ) B ( . P(A cup B cup C) leq P(A)+P(B)+P(C) ) C. ( P(text { exactly one of } A, B, C text { occur }) leq P(A)+P(B)+ ) ( P(C)-P(B cap C)-P(C cap A)-P(A cap B) ) D. ( P(A text { and at least one of } B, C text { occurs }) leq P(A cap B)+ ) ( P(A cap C) ) | 12 |

1107 | 27. A computer producing factory has only two plants T, and T, Plant T, produces 20% and plant T, produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective given that it is produced in plant T) = 10P (computer turns out to be defective given that it is produced in plant T.), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T, is (JEE Adv. 2016) -36 75 (a) (b) (c) (d) noontira inteners y Yand 7 | 12 |

1108 | If ( frac{1+3 p}{3}, frac{1-2 p}{2} ) are probabilities of two mutually exclusive event, then ( p ) lies in the interval ( ^{A} cdotleft[-frac{1}{3}, frac{1}{2}right] ) B ( cdotleft(-frac{1}{2}, frac{1}{2}right) ) ( ^{mathbf{C}} cdotleft[-frac{1}{2}, frac{2}{3}right] ) D. ( left(-frac{1}{3}, frac{2}{3}right) ) | 12 |

1109 | In a single throw of three dice, if the probability of getting a total of 17 or 18 is ( frac{1}{a} . ) Find ( a ) | 12 |

1110 | Two numbers ( b ) and ( c ) are chosen at random (with replacement) from the numbers 1,2,3,4,5,6,7,8 and ( 9 . ) The probability that ( x^{2}+b x+c>0 ) for all ( c in boldsymbol{R} ) is ( frac{mathbf{4} k}{81} . ) Find the value of ( boldsymbol{k} ? ) | 12 |

1111 | Bag ( I ) contains 2 blacks and 8 red balls, bag IIcontains 7 black and 3 red balls and bag ( I I I ) contains 5 black and ( 5 v ) red balls. One bage is chosen at random and a ball is drawn from it which is found to bered. Find the probability that the ball is drawn from bag ( I I ) | 12 |

1112 | An experiment involves rolling a pair of dice and recording the numbers that come up describe the following events: ( A: ) the sum is greater than 8 ( mathrm{B}: 2 ) occurs on either die ( mathrm{C}: ) the sum is at least 7 and a multiple of 3 Which pairs of these events are mutually exclusive? | 12 |

1113 | If ( A ) and ( B ) are mutually exclusive events, then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) equals ( mathbf{A} cdot mathbf{0} ) B. ( frac{1}{2} ) c. D. | 12 |

1114 | Consider the experiment of throwing a die, if a multiple of 3 comes up, thrown the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3 ‘. | 12 |

1115 | The probability of student ( A ) passing an examination is ( frac{2}{9} ) and of students, ( B ) passing is ( frac{5}{9} . ) Assuming the two events: ( A ) passes’. ( B ) passes’ as independent, find the probability of both passing the examination. | 12 |

1116 | ( A ) box ( ^{prime} A^{prime} ) contains 2 white, 3 red and 2 black balls. Another box ‘ ( B^{prime} ) contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box’ ( B^{prime} ) is A ( cdot frac{7}{16} ) в. ( frac{9}{32} ) ( c cdot frac{7}{8} ) D. ( frac{9}{16} ) | 12 |

1117 | For two events ( boldsymbol{A} ) and ( boldsymbol{B}, ) if ( boldsymbol{p}(boldsymbol{A})= ) ( boldsymbol{p}(boldsymbol{A} mid boldsymbol{B})=frac{1}{4} ) and ( boldsymbol{p}(boldsymbol{B} mid boldsymbol{A})=frac{1}{2}, ) then ( Pleft(frac{bar{B}}{bar{A}}right)=frac{m}{n} ) where ( m+n= ) | 12 |

1118 | The probability that an event A happens in one trial of an experimentis 0.4. Three independent trials of the experiment are performed. The probability that the event A happens at least once is (1980) (a) 0.936 (b) 0.784 (c) 0.904 (d) none of these т с | 12 |

1119 | In 16 throws of a die getting an even number is considered a success, then the variance of the success is A . 4 B. 6 ( c cdot 2 ) D. 256 | 12 |

1120 | паре спасtwoo пооооп и по In 65 throws of a dice, 5 is obtained 22 times. Now, in a 22 random throw of a dice, the probability of getting 5 is a | 11 |

1121 | If heads means one and tail means two, then coefficients of quadratic equation ( a x^{2}+b x+c=0 ) are chosen by tossing three fair coins. The probability that roots of the equation are imaginary is A ( cdot frac{5}{8} ) B. ( frac{3}{8} ) ( c cdot frac{7}{8} ) D. | 12 |

1122 | There are 44 students in class ( X ) of ( a ) school of whom 32 are boys and 12 are girls. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then he puts cards in a bag and stir them thoroughly. He then draws one card from the bag. What is the probability that the name written on the card is the name of a girl? A ( cdot frac{1}{11} ) B. ( frac{5}{11} ) ( c cdot frac{7}{11} ) D. None of these | 12 |

1123 | Arun and Tarun appeared for an interview for two vacancies. The probability of Arun’s selection is ( frac{1}{4} ) and that of Tarun’s rejection is ( frac{2}{3} . ) Find the probability that at least one of them will be selected. | 12 |

1124 | Two numbers are selected at random from integers 1 through ( 9 . ) If the sum is even, find the probability that both the numbers are odd. | 12 |

1125 | The terms ‘chance’ and ‘probability’ are synonymous. A . True B. False c. Both D. None of above | 12 |

1126 | If a fair die is rolled 4 times, then what is the probability that there are at least 2 sixes? A ( cdot frac{19}{144} ) в. ( frac{25}{216} ) c. ( frac{125}{216} ) D. ( frac{175}{216} ) | 12 |

1127 | Two different dice are tossed together. Find the probability of the sum of no’s appearing on two dice is 5 A ( cdot frac{1}{36} ) в. ( frac{1}{18} ) c. ( frac{1}{9} ) D. ( frac{1}{6} ) | 12 |

1128 | A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wring envelope. | 12 |

1129 | Given that the two numbers appearin the probability of the event ‘the sum | 12 |

1130 | Choosing a marble from a jar and landing on heads after tossing a coin is an act of A. experiment B. space c. sample D. event | 12 |

1131 | A random variable ( boldsymbol{X} ) is binomially distributed with mean 12 and variance 8. The parameters of the distribution are ( ldots . . & ldots . ) A ( cdot_{36, frac{2}{3}} ) в. ( _{36, frac{1}{3}} ) c. ( _{24, frac{1}{3}} ) D. ( 24, frac{2}{3} ) | 12 |

1132 | If two coins are tossed, then find the probability of the event that at the most one tail turns up. | 12 |

1133 | Probability is 0.45 that a dealer will sell at least 20 television sets during a day, and the probability is 0.74 that he will sell less that 24 televisions. The probability that he will sell 20,21,22 or 23 televisions during the day, is A . 0.19 в. 0.32 c. 0.21 D. None of these | 12 |

1134 | What is the total number of candidates at an examination, if ( 31 % ) fail and the number of failing students is 248 A. 800 B. 900 c. 1,000 D. 1,100 | 12 |

1135 | Suppose a girl throws a die. If she gets a 5 or ( 6, ) she tosses a coin 3 times and notes the number of heads. If she gets 1,2,3 or 4 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,3 or 4 with the die? ( mathbf{A} cdot frac{1}{9} ) в. ( frac{5}{16} ) c. ( frac{2}{13} ) D. ( frac{8}{11} ) | 12 |

1136 | A bag contains a certain number of balls, some of which are white;a ball is drawn and replaced, another is then drawn and replaced’ and so on. If p be the chance of white balls that is most likely to have been drawn in n trials. For ( p=frac{1}{2} ) and ( n=12, ) the number of white balls required to be drawn is ( k ). Find the value of ( k ) | 12 |

1137 | A box contains 20 cards marked with numbers 1 to ( 20 . ) One card os drwan from the box at random. What is the probability of the following events: (1) That number on the card is a prime number, (2) The number on the card is a perfect square. | 12 |

1138 | The probability that a student is not a swimmer is ( frac{1}{5} . ) Then the probability that out of five students, four are swimmers is ( ^{mathbf{A}} cdot_{^{5}} C_{4}left(frac{4}{5}right)^{4} frac{1}{5} ) ( ^{mathrm{B}}left(frac{4}{5}right)^{4} frac{1}{5} ) ( ^{mathbf{c}} cdot_{^{5}} C_{1} frac{1}{5}left(frac{4}{5}right)^{4} ) D. none of these. | 12 |

1139 | If ( A ) and ( B ) are two events such that ( boldsymbol{A} subset boldsymbol{B} ) and ( boldsymbol{P}(boldsymbol{B}) neq 0, ) then which of the following is correct? This question has multiple correct options ( ^{mathbf{A}} cdot p(A mid B)=frac{P(B)}{P(A)} ) B cdot ( P(A mid B)<P(A) ) C ( cdot P(A mid B) geq P(A) ) D. None of these | 12 |

1140 | If a random variable X takes values ( (-1)^{k} 2^{k} / k ; k=1,2,3, dots . ) with probabilities ( boldsymbol{P}(boldsymbol{X}=boldsymbol{k})=frac{mathbf{1}}{mathbf{2}^{k}} ) then ( E(X)= ) A ( . log 2 ) в. ( log e ) c. ( log left(frac{1}{2}right) ) D. ( log left(frac{1}{4}right) ) | 12 |

1141 | Two dice are thrown together. Find the probability of getting a sum equal to 8 | 12 |

1142 | An die is tossed twice. Find the probability of getting 4,5 or 6 on the toss and 1,2,3 or 4 on the second toss. | 12 |

1143 | Two cards are drawn from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces. | 12 |

1144 | Let ( X ) represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of ( X ? ) в. 0,2,4,6 c. 6,7,7,2 D. 6,4,2,0 | 12 |

1145 | Consider two events ( A ) and ( B ) of an experiment where ( P(A cap B)=frac{1}{4} ) and ( P(B)=frac{1}{2}, ) then ( P(A) ) cannot exceed ( A cdot frac{1}{2} ) B. ( frac{2}{3} ) ( c cdot frac{3}{4} ) D. | 12 |

1146 | Suppose ( 5 % ) of men and ( 0.25 % ) of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females. | 12 |

1147 | An event ( X ) can take place in conjunction with any one of the mutually exclusive and exhaustive events ( A, B ) and ( C . ) If ( A, B, C ) are equiprobable and the probability of ( X ) is ( 5 / 12 ) and the probability of ( X ) taking place when A has happened is 3/8 while it is ( 1 / 4 ) when ( mathrm{B} ) has taken place, then the probability of ( X ) taking place on conjunction with ( mathrm{C} ) is A . ( 5 / 8 ) в. ( 3 / 8 ) ( c cdot 5 / 24 ) D. none of these | 12 |

1148 | Find the number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon. | 12 |

1149 | Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that the first ball is black and the second is red. | 12 |

1150 | In a bolt factory, machines ( A, B ) and ( C ) manufacture ( 25 %, 35 % ) and ( 40 % ) respectively of the total number of bolts. The percentage of defective bolts among the manufactured bolts is ( 5 % ) for ( A, 4 % ) for ( B ) and ( 2 % ) for ( C . ) A bolt is drawn randomly from the manufactured products and is found to be defective then This question has multiple correct options A. the probability that the selected bolt is defective ( = ) 0.0345 B. the probability that the defective bolt was manufactured by machine ( A=frac{25}{69} ) C. the probability that the defective bolt was manufactured by machine ( B=frac{28}{69} ) D. the probability that the defective bolt was manufactured by machine ( C=frac{16}{69} ) | 12 |

1151 | The mean weight of 500 male students in a certain college is 151 pounds and the standard deviation is 15 pounds. Assuming the weights are normally distributed, find the approximate number of students weighing. (i) between 120 and 155 pounds, [ begin{array}{llll} z & 0.2667 & 2.067 & 2.2667 \ & & & \ text { Area } & 0.1026 & 0.4803 & 0.4881 end{array} ] (ii) more than 185 pounds. | 12 |

1152 | In a hostel, ( 60 % ) of the students read Hindi newspaper, ( 40 % ) read English newspaper and ( 20 % ) read both Hindi and English newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English newspapers. A ( cdot frac{1}{5} ) B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) D. ( frac{4}{5} ) | 12 |

1153 | A pack of cards is counted with face downwards. It is found that one card is missing, One card is drawn and is found to be red. Find the probability that the missing card is red. | 12 |

1154 | 12. The po The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S) (a) 1/8 (6) 1/4 (c) 1/2 (d) 213 | 12 |

1155 | A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is- A ( cdot frac{1}{729} ) в. ( frac{8}{9} ) c. ( frac{8}{729} ) D. ( frac{8}{243} ) | 12 |

1156 | When a die is thrown, list the outcomes of an event of getting a) A prime number b) A number greater than 6 | 12 |

1157 | In a World Cup final match against Srilanka, for six times Sachin Tendulkar hits a six out of 30 balls he plays. What is the probability that in a given throw the ball does not hit a six? A ( cdot frac{1}{4} ) B. ( c cdot frac{4}{5} ) D. ( frac{3}{4} ) | 12 |

1158 | Probability of getting a prime (or) composite is A. Mutually exclusive B. Likely c. 0 D. None | 12 |

1159 | Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20 | 12 |

1160 | A letter is known to have come either from ( L O N D O N ) or ( C L I F T O N ; ) on the postmark only the two consecutive letters ( boldsymbol{O} boldsymbol{N} ) are ellegible. The probability that it came from ( L O N D O N ) is A ( cdot frac{5}{17} ) в. ( frac{12}{17} ) c. ( frac{17}{30} ) D. ( frac{3}{5} ) | 12 |

1161 | 2K coins (K is an integer) each with probability P(O ( ^{A} cdot frac{K}{2 K+1} ) в. ( frac{K+1}{2 K} ) c. ( frac{K+1}{2 K+1} ) D. ( frac{2 K}{K+1} ) | 12 |

1162 | If ( A ) and ( B ) are mutually exclusive such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

1163 | Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket? | 12 |

1164 | Three of the six vertices of regular hexagon are chosen at random. The probability that the triangle with these vertices is equilateral, equals A. ( 1 / 2 ) в. ( 1 / 5 ) c. ( 1 / 10 ) D. ( 1 / 20 ) | 12 |

1165 | In an entrance test, there are multiple choice questions. There are four possible options of which one is correct. The probability that a student knows the answer to a question is ( 90 % ). If he gets the correct answer to a question, then the probability that he was guessing is A ( cdot frac{1}{37} ) B. ( frac{36}{37} ) ( c cdot frac{1}{4} ) D. ( frac{1}{49} ) | 12 |

1166 | For any two independent events ( boldsymbol{E}_{1} ) and ( boldsymbol{E}_{2}, boldsymbol{P}left{left(boldsymbol{E}_{1} cup boldsymbol{E}_{2}right) cap(overline{boldsymbol{E}_{1}}) cap(overline{boldsymbol{E}_{2}})right} ) is ( A cdot leq frac{1}{4} ) B. ( >frac{1}{4} ) ( c cdot geq frac{1}{2} ) D. None of these | 12 |

1167 | Q Type your question in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below : No. of faulty packet Number of packets 0 1 2 3 4 Total number of packets 500 If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault? A . 0.5 B. 0.6 c. 0.8 D. 0.9 | 12 |

1168 | Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( P(B / A) ) | 12 |

1169 | A screw factory has two machines, the M1, which is old, and does ( 75 % ) of all the screws, and the M2, newer but small, that does ( 25 % ) of the screws. The ( mathrm{M} ) does ( 4 % ) of defective screws, while the M2 just does ( 2 % ) of defective screws. If we choose a screw at random: what is the probability that it turns out to be defective? A. 0.035 в. 0.045 c. 0.015 D. None of these | 12 |

1170 | For two events, ( A ) and ( B ), it is given that ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{3}}{mathbf{5}}, boldsymbol{P}(boldsymbol{B})=frac{mathbf{3}}{mathbf{1 0}} ) and ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})= ) ( mathbf{2} ) ( frac{2}{3} . ) If ( bar{A} ) and ( bar{B} ) are the complementary events of ( A ) and ( B ), then what is ( P(bar{A} mid bar{B}) ) equal to? ( A cdot frac{3}{7} ) B. ( frac{3}{4} ) ( c cdot frac{1}{3} ) D. | 12 |

1171 | In a class of 55 students, the number of students studying in different subject are, 23 in Mathematics, 24 in physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. Find the number of students who have taken exactly one subject. | 12 |

1172 | A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is A ( cdot frac{13}{3^{5}} ) в. ( frac{11}{3^{5}} ) c. ( frac{10}{3^{5}} ) D. ( frac{17}{3^{5}} ) | 12 |

1173 | The probability of getting the rotten egg from a lot of 400 eggs is ( 0.035 . ) Find the number of rotten eggs in the lot. | 12 |

1174 | If the probability of ( x ) to fail in the examination is 0.3 and that for ( Y ) is 0.2 then the probability that either ( boldsymbol{X} ) or ( boldsymbol{Y} ) fail in the examination is A . 0.5 B. 0.44 ( c .0 .6 ) D. None of these | 12 |

1175 | In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in either Hindi or Mathematics but not in English? A . 99 в. 107 c. 125 D. 130 | 12 |

1176 | A die is tossed twice. Getting an odd number is termed a success. The probability distribution of number of successes ( (X) ) is formed. Then its mean, variance are A ( cdot 1, frac{1}{2} ) B. ( frac{1}{2}, 1 ) c. ( frac{1}{2}, frac{1}{2} ) D. 1,1 | 12 |

1177 | Which of the following is/are true? A. Profitability Index (PI) is a variation of the NPV rule B. Even in case of mutually exclusive projects a conflict of ranking will not arise between PI and NPV C. A project should be accepted when both PI and NPV are positive D. All of the above E. Both (A) and (C) above | 12 |

1178 | Three balanced coins are tossed simultaneously. If ( X ) denotes the number of heads, find probability distribution of ( boldsymbol{X} ) | 12 |

1179 | The probability of an impossible event is ( mathbf{A} cdot mathbf{3} ) B. c. 1 ( D ) | 12 |

1180 | We draw two cards from a deck of shuffled cards without replacement. Find the probability of getting the second card a queen. A ( cdot frac{1}{13} ) в. ( frac{2}{13} ) ( c cdot frac{5}{13} ) D. None of these | 12 |

1181 | A bag contains some white and some black balls, all combinations of balls being equally likely. The total number of balls in the bag is ( 10 . ) If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is A ( cdot frac{14}{55} ) B. ( frac{12}{55} ) ( c cdot frac{2}{55} ) D. ( frac{8}{55} ) | 12 |

1182 | There are 5 cards in a box with numbers 1 to5 written on them. If 2 cards are picked out from the box, write all the possible outcomes and find the probpossible ability of getting both even numbers. | 12 |

1183 | 3. In a throw of a dice, the probability of getting an even number is the same as that of getting an odd number. | 11 |

1184 | ( A=x / x ) is a two digit number, which divisible by ( 2(text { or }) 3 ) and ( x leq 50, B= ) ( x / x ) is a two digit number, which divisible by 6 and ( x leq 50 ).Find ( n(A cup B)=? ) ( n(A cap B)=? ) | 12 |

1185 | If head means one and tail means two then coefficients of quadratic equation ( a x^{2}+b x+c=0 ) are chosen by tossing three fair coins. The probability that roots of the equation are imaginary is A ( cdot frac{5}{8} ) B. ( frac{3}{8} ) ( c cdot frac{7}{8} ) D. | 12 |

1186 | Three six-faced fair dice are thrown together let ( P(k) ) denote the probability that the sum of the numbers appearing on the dice is ( k(9 leq k leq 4) ). Find 54 s where ( boldsymbol{S}=sum_{boldsymbol{k}=mathbf{9}}^{mathbf{1 4}} boldsymbol{P}(boldsymbol{k}) ) | 12 |

1187 | The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is ( 0.1 . ) If the probability of passing the English examination is ( 0.75, ) what is the probability of passing the Hindi examination? | 12 |

1188 | The term law of total probability is sometimes taken to mean the A. Law of total expectation B. Law of alternatives c. Law of variance D. None of these | 12 |

1189 | An electronic machine chooses random numbers from I to 30. What is the probability that the number chosen is an even number? (a) 15/30 (b) 1/10 (c) 1/6 (d) 1/2 | 11 |

1190 | If ( X ) follows a binomial distribution with parameters ( n=8 ) and ( p=frac{1}{2}, ) then ( boldsymbol{P}(|boldsymbol{X}-mathbf{4}| leq mathbf{2}) ) is A ( cdot frac{119}{128} ) в. ( frac{119}{228} ) c. ( frac{19}{128} ) D. ( frac{18}{28} ) | 12 |

1191 | One ticket is selected randomly from the set of 100 tickets numbered as ( {00,01,02,03,04,05, ldots, 98,99} . E_{1} ) and ( E_{2} ) denote the sum and product of the digits of the number of the selected ticket. The value of ( boldsymbol{P}left(frac{boldsymbol{E}_{1}=boldsymbol{9}}{boldsymbol{E}_{2}=mathbf{0}}right) ) is A ( cdot frac{1}{19} ) B. ( frac{2}{19} ) ( c cdot frac{3}{19} ) D. ( frac{1}{18} ) | 12 |

1192 | Three different coins are tossed together find the probability of i) Exactly two heads ii) At least one tails ii) Almost two heads iv) At most two tails v) At least two tails vi) At most one head vii) At least one head | 12 |

1193 | An insurance company issued 3000 scooters, 4000 cars and 5000 trucks. The probabilities of the accident involving a scooter, a car and a truck are 0.02,0.03 and 0.04 respectively. One of the insured vehicles meet with an accident. Find the probability that it is a (i) scooter (ii) car (iii) truck. | 12 |

1194 | An unbiased coin is tossed. if the result is a head, a pair of unbiased dice is rolled & the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered ( 2,3,4, dots, 12 ) is picked ( & ) the number on the card is noted. What is the probability that the noted number is either 7 or ( 8 ? ) A. 0.24 в. 0.27 ( c .0 .3 ) D. 0.31 | 12 |

1195 | The probability distribution of a discrete random variable ( X ) is: [ boldsymbol{X}=boldsymbol{x} quad mathbf{1} quad boldsymbol{2} quad boldsymbol{3} ] ( P(X= ) ( x) ) [ 3 k ] ( 4 k ) ( k quad 2 k ) [ text { Find } P(X leq 4) ] ( mathbf{A} cdot frac{2}{3} ) B. ( frac{3}{4} ) ( c cdot frac{4}{5} ) D. ( frac{5}{6} ) | 12 |

1196 | If ( A ) and ( B ) are two mutually exclusive events, then This question has multiple correct options ( mathbf{A} cdot P(A) leq P(bar{B}) ) B ( . P(bar{A} cap bar{B})=P(bar{A})-P(B) ) ( mathbf{c} cdot P(bar{A} cup bar{B})=0 ) D . ( P(bar{A} cap B)=P(B) ) | 12 |

1197 | Which of the following are correct regarding normal distribution curve? (i) Symmetrical about the line ( boldsymbol{X}=boldsymbol{mu} ) (Mean) (ii) Mean ( = ) Median ( = ) Mode (iii) Unimodal (iv) Points of inflexion are at ( boldsymbol{X}=boldsymbol{mu} pm boldsymbol{sigma} ) A . (i), (ii) B. (ii), (iv) c. (i), (ii), (iii) D. All of these | 12 |

1198 | Three cards are drawn at random (without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution. | 12 |

1199 | 30. sum as well as Iftwo different numbers are taken from the set (0.1 …….., 10), then the probability that their sum as we absolute difference are both multiple of 4, is : [JEE M 2017 (b) ante A Band C | 11 |

1200 | If the papers of 4 students can be checked by any one of the seven teachers, then the probability that all the four papers are checked by exactly two teachers is A ( cdot frac{6}{49} ) B. ( frac{2}{7} ) c. ( frac{32}{343} ) D. ( frac{2}{343} ) | 12 |

1201 | In a factory machine ( boldsymbol{A} ) produce ( mathbf{3 0 %} ) of the total output, machine ( B ) produced ( 25 % ) and the machine ( C ) produced the remaining output. If defective items produced by machine ( A, B ) and ( C ) are ( 1 %, 1.2 %, 2 % ) respectively. Three machine working together produced 10000 item in a day. An item is drawn at random from a day’s output and found to be defective. Find the probability that it was produced by machine ( boldsymbol{B} ) ? | 12 |

1202 | A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? A ( cdot frac{3}{4} ) B. ( frac{4}{7} ) ( c cdot frac{1}{8} ) D. | 12 |

1203 | In a particular section of class ( 1 X, 40 ) students were asked about the month of their birth and following graph was prepared for data so obtained: Find the probability that a student of | 12 |

1204 | A dice is thrown twice. A success is an even number on each throw. Find the probability distribution of the number of successes. | 12 |

1205 | For 3 events ( A, B ) and ( C, P( ) exactly one of the events ( A text { or } B text { occurs })=P( ) exactly one of the events ( mathrm{B} text { or } mathrm{C} text { occurs })=mathrm{P}( ) exactly one of the events ( C text { or } A text { occurs })=p & P ) (all the three events occurs simultaneously) ( =p^{2} . ) Where ( o<p<frac{1}{2} ) then the probability of at lest one of three events, ( A, B & C ) occurring is A ( cdot frac{3 p+2 p^{2}}{2} ) B. ( frac{p+2 p^{2}}{2} ) c. ( frac{3 p+p^{2}}{2} ) D. ( frac{3 p+2 p^{2}}{4} ) | 12 |

1206 | Let ( A ) and ( B ) be two events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})- ) ( boldsymbol{P}(boldsymbol{A}) boldsymbol{P}(boldsymbol{B}) . ) If ( boldsymbol{0}<boldsymbol{P}(boldsymbol{A})<1 ) and ( boldsymbol{0}< ) ( boldsymbol{P}(boldsymbol{B})<1, ) then ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})^{prime} ) is equal to A ( cdot 1-P(A) ) B . ( 1-Pleft(A^{prime}right) ) c. ( 1-P(A) P(B) ) D cdot ( [1-P(A)] Pleft(B^{prime}right) ) ( E ) | 12 |

1207 | 13. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals (1995S) (a) 1/2 (b) 1/5 – (c) 1/10 (d) 1/20 | 11 |

1208 | In a factory which manufactures bolts, machines ( A, B ) and ( C ) manufacture ( 30 %, 50 % ) and ( 20 % ) of the bolts respectively. Of their output ( 3 %, 4 % ) and ( 1 % ) respectively are defective bolts. bolt is drawn at random from the product and is found to be defective Find the probability that this is not manufactured by machine B. | 12 |

1209 | A player throws 2 ordinary die with faces numbered 1 to 6. What is the probability of obtaining a total score of atmost ( 6 ? ) A ( cdot 12 / 36 ) B. ( 16 / 36 ) c. ( 15 / 36 ) D. ( 10 / 36 ) | 12 |

1210 | The probability of happening of an event is ( 45 % . ) The probability of an event is : A . 45 B. 4. ( c cdot 0.45 ) D. 0.045 | 12 |

1211 | A bag contains 3 red and 3 green balls and a person draws out 3 at random. He then drops 3 blue balls into the bag and again draws out 3 at random. The chance that the 3 later balls being all of different colors is A . ( 15 % ) B . 20% c. ( 60 % ) D. 40% | 12 |

1212 | The probability that in a group of ( N ) people at least two will have the same birthday is A ( cdot_{1-frac{(365) !}{(365)^{N}(365-N) !}} ) В ( cdot_{1+frac{(365) !}{(365)^{N}(365-N) !}} ) c. ( _{1-} frac{(365) !}{(365)^{N}(365+N) !} ) D. None of these | 12 |

1213 | If ( A ) and ( B ) are any two events such that ( P(A)=frac{2}{5} ) and ( P(A cap B)=frac{3}{20}, ) then the condition probability, ( boldsymbol{P}left(boldsymbol{A} mid boldsymbol{A}^{prime} cupright. ) ( left.B^{prime}right) ), where ( A^{prime} ) denotes the complement of ( A, ) is equal to: A ( cdot frac{5}{17} ) в. ( frac{11}{20} ) ( c cdot frac{1}{4} ) D. ( frac{8}{17} ) | 12 |

1214 | A seven digit number is formed by using 0,1,2,3,4,8,9 without repetition. Then the probability that it is divisible by 4 is A ( cdot frac{53 times 4 !}{5 times 6 !} ! ) в. ( frac{53}{180} ) c. ( frac{53}{6 times 6 !} ) D. None of these | 12 |

1215 | Obtain the probability distribution of the number of sixes in two tosses of a fair die | 12 |

1216 | If ( P(1) ) be the probability of an event ( A ) then A. ( -1 leq P(1) leq 1 ) B. ( 0 leq P(1)<0.5 ) c. ( 0 leq P(1) leq 1 ) D. None of these | 12 |

1217 | Die ( A ) has 4 red and 2 white faces where as die ( B ) has two red and 4 white faces. ( A ) fair coin is tossed. If head turns up, the game continues by throwing die ( A ) if tail turns up then die ( B ) is to be used. If the first two throws resulted in red, what is the probability of getting red face at the third throw? ( A cdot frac{2}{5} ) B. ( frac{1}{5} ) ( c cdot frac{3}{5} ) D. ( frac{1}{2} ) | 12 |

1218 | The probability that, on the examination day, the student ( S_{1} ) gets the previously allotted seat ( R_{1} ) and NONE of the remaining students gets the seat previously allotted to him/her is? ( A cdot frac{3}{40} ) B. ( frac{1}{8} ) c. ( frac{7}{40} ) D. ( frac{1}{5} ) | 12 |

1219 | When two dice are thrown, list the number outcomes of an even of getting equal to 8 A .2 B. 3 ( c cdot 4 ) D. 5 | 12 |

1220 | In a survey of 600 students in a school, (i) 160 students were found to be taking Tea 215 taking Coffee, 150 were taking both Tea and Coffee. (ii) 150 students were found to be taking tea and 225 taking coffee, 100 were taking both Tea and Coffee. Find how many students were taking neither tea nor coffee? | 12 |

1221 | Not more than one fuses. | 12 |

1222 | The act of throwing a die is called an A . outcomes B. event c. experiment D. sample | 12 |

1223 | Given two independence events ( A ) and ( B, ) such that ( P(A)=0.3 ) and ( P(B)= ) 0.6. Find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) | 12 |

1224 | A bag contains ( n+1 ) coins. It is known that one of these coins has heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that the toss results in heads is ( 7 / 12, ) find ( n ) | 12 |

1225 | Two dice are thrown The events ( A, B ) and ( C ) are as follows: A : getting an even number on the first die B : getting an odd number on the first die C : getting the sum of the numbers on the dice ( leq 5 ) Describe the events (i) ( A^{prime} ) (ii) not ( boldsymbol{B} ) (iii) ( boldsymbol{A} ) or ( boldsymbol{B} ) (iv) ( A ) and ( B ) (v) ( A ) but not ( C ) (vi) ( B ) or ( C ) (vii) ( B ) and ( C ) (viii) ( boldsymbol{A} cap boldsymbol{B}^{prime} cap boldsymbol{C}^{prime} ) | 12 |

1226 | The probability distribution of a random variable ( X ) is given below: [ begin{array}{lllll} mathrm{x}: & 0 & 1 & 2 & 3 \ mathrm{P}(mathrm{x}): & mathrm{k} & frac{k}{2} & frac{k}{4} & frac{k}{8} end{array} ] Determine the value of ( X, ) if ( k=frac{8}{X} ) | 12 |

1227 | How many different numbers, greater than 50000 can be formed with the ( operatorname{digits} mathbf{0}, mathbf{1}, mathbf{1}, mathbf{5}, mathbf{9} ) | 12 |

1228 | DIA 2 SUP 6. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb? | 11 |

1229 | ( A ) and ( B ) are two independent events. The probability that both ( A ) and ( B ) occur is ( frac{1}{6} ) and the probability that neither of them occurs is ( frac{1}{3} . ) The probability of occurrence of A is? A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{5}{6} ) D. | 12 |

1230 | A lot of contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability that the lot contains exactly 3 defective articles is ( 0.6 . ) Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelfth testing? A ( cdot frac{99}{1900} ) в. ( frac{99}{950} ) c. ( frac{198}{1900} ) D. ( frac{99}{1000} ) | 12 |

1231 | Two events ( A ) and ( B ) are such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} ) ( boldsymbol{B})=mathbf{0 . 5 . F i n d} boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) ( mathbf{A} cdot mathbf{0} ) B. 0.2 ( c .0 .3 ) D. 0.5 | 12 |

1232 | Two numbers are selected at random (without replacement) the first six positive integers. Let ( X ) denote the larger of the two numbers obtained. Find ( boldsymbol{E}(boldsymbol{X}) ) | 12 |

1233 | If it rains on Republic Day parade an Auto Riksha earns Rs. ( 240, ) on the other hand it does not rain he loses Rs. ( 60 . ) The probability of rain on Republic Day parade is ( 0.6 . ) What is the value of expected income of an Auto Riksha on Republic Day parade? A . Rs. 150 B. Rs. 45 c. Rs. 120 D. Rs. 10 | 12 |

1234 | ( A ) can hit target three times in six shots, ( B ) can hit target 2 times in six shots and ( C ) can hit target 4 times in a 6 shots. They fix a ball. But what is the probability that they hit ball in atleast two shots. | 12 |

1235 | The probability that ( A ) hit a target is ( 1 / 4 ) and the probability that ( B ) hits the target is ( 1 / 3 . ) If each of them fired once, what is the probability that the target will be hit atleast once? | 12 |

1236 | There are 3 men and 2 women. a ‘Gramswachhatta Abhiyan’ committee of two is to be formed: ( P ) is event that the committee should contain at least one woman. ( Q ) is event that the committee should contain one man and one women. ( R ) is the event there should not be a women in the committee. ( S ) is the sample space. Which of the following options is correct? A ( . n(S)=10, n(P)=7, n(Q)=1, n(R)=3 ) В. ( n(S)=10, n(P)=7, n(Q)=3, n(R)=3 ) c. ( n(S)=10, n(P)=7, n(Q)=2, n(R)=3 ) D. ( n(S)=10, n(P)=7, n(Q)=6, n(R)=3 ) | 12 |

1237 | In a hockey match, both teams ( A ) and ( B ) scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team ( A ) was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not. | 12 |

1238 | Two coins are tossed simultaneously. Write the sample space ( S ) and the number of sample point ( n(S) . A ) is the event of getting at least one head. Write the event ( A ) in set notation and find ( boldsymbol{n}(boldsymbol{A}) ) | 12 |

1239 | The probability mass function (p.m.f) of ( X ) is given below: [ begin{array}{lllll} X=x & 1 & 2 & 3 \ P(X=x) & frac{1}{5} & frac{2}{5} & frac{2}{5} end{array} ] | 12 |

1240 | If ( boldsymbol{E} ) and ( boldsymbol{F} ) are independent events such that ( boldsymbol{P}(boldsymbol{E})=mathbf{0 . 7} ) and ( boldsymbol{P}(boldsymbol{F})=mathbf{0 . 3}, ) then ( mathrm{P} ) ( (boldsymbol{E} cap boldsymbol{F}) ) A . 0.4 B. c. 0.21 D. None | 12 |

1241 | Addition Theorem of Probability states that for any two events ( A ) and ( B ) ( mathbf{A} cdot P(A cup B)=P(A)+P(B) ) B ( cdot P(A cup B)=P(A)+P(B)+P(A cap B) ) ( mathbf{c} cdot P(A cup B)=P(A)+P(B)-P(A cap B) ) D ( . P(A cup B)=P(A) times P(B) ) | 12 |

1242 | 6. For any For any two events A and B in a sample space (1991,- 2 Marks) (a) P(A/B) P(A)+PB)- P(B) +0 is always true P(B) (b) P( AB) = P(A) – P(AB) does not hold © P(AUB) = 1- P(Ā) P(B), if A and B are independent (d) P(AUB) = 1- PĀ) P(B), if A and B are disjoint. | 12 |

1243 | If ( A, B ) are two events with ( P(A cup B)= ) ( mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 5}, ) then find the value of ( boldsymbol{P}left(boldsymbol{A}^{C}right)+boldsymbol{P}left(boldsymbol{B}^{C}right) ) | 12 |

1244 | If ( A ) and ( B ) are mutually exclusive such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) ) | 12 |

1245 | Statement 1: The variance of first n even natural numbers is ( frac{mathbf{n}^{2}-mathbf{1}}{mathbf{4}} ) Statement 2: The sum of first n natural numbers is ( frac{mathbf{n}(mathbf{n}+mathbf{1})}{mathbf{2}} ) and the sum of squares of first n natural numbers is ( frac{mathbf{n}(mathbf{n}+mathbf{1})(mathbf{2 n}+mathbf{1})}{mathbf{6}} ) A. Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1 B. Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1 c. Statement 1 is true, Statement 2 is false D. Statement 1 is false, Statement 2 is true | 12 |

1246 | 11. A randem variable thans Poisson distribution with mean> A random variable X has Poisson distribution with mean 2. Then P(X>1.5) equals [2005] (b) 0 | 12 |

1247 | 14. Two aeroplanes I and II probabilities of I and respectively. The aeroplanes I and II bomb a target in succession. The habilities of I and Il scoring a hit correctly are 0.3 and 0.2 ectively. The second plane will bomb only if the first misses the target. The probability that the target the second plane is [2007] (a) 0.2 (b) 0.7 (c) 0.06 (d) 0.14 cs : | 12 |

1248 | An ordinary pack of 52 cards is well shuffled. The top card is then turned over. What is the probability that the top card is a black card. | 12 |

1249 | 28. Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is 36 (a) (d) | 11 |

1250 | An unbiased normal coin is tossed ( n ) times. Let ( E_{1}: ) event that both heads and tails are present in ( n ) tosses. ( E_{2} ) :event that the coin shows up heads at most once. The value of ( n ) for which ( E_{1} ) and ( E_{2} ) are independent is ( A ) B. 2 ( c cdot 3 ) D. 4 | 12 |

1251 | Which of the following is not the outcome while Spinning a wheel ( A ) B. B ( c cdot c ) ( D ) | 12 |

1252 | A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a jack, a queen or a king. | 12 |

1253 | Three coins are tossed simultaneously: ( P ) is the event of getting at least two heads. ( Q ) is the event of getting no heads. ( R ) is the event of getting heads on second coin. Which of the following pairs is mutually exclusive? This question has multiple correct options A. ( Q, R ) в. ( Q, P ) c. ( P, R ) D. None of these | 12 |

1254 | If ( Pleft(E_{k}right) propto k ) for ( 0 leq k leq n, ) then the probability that ( X ) is the only student to pass the examination is A ( cdot frac{3}{n(n+1)} ) в. ( frac{6}{n(n+1)(2 n+1)} ) ( c cdot frac{1}{n} ) D. ( frac{1}{n(2 n+1)} ) | 12 |

1255 | The numbers 1,2,3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other without replacement. Describe the following events: ( A= ) The number on the first slip is larger than the one on the second slip. ( B= ) The number on the second slip is greater than ( 2 quad C= ) The sum of the numbers on the two slip is 6 or 7 ( D= ) The number on the second slips is twice that on the first slip. Which pair (s) of events is (are) mutually exclusive | 12 |

1256 | If ( mathrm{S} ) is the sample space for the event ( mathrm{A} ) then find the correct alternative from the following: A ( .0 geq P(A) geq 1 ) B. ( 0 leq P(A)<1 ) c. ( 0<P(A) leq 1 ) D. ( 0 leq P(A) leq 1 ) | 12 |

1257 | Difference between sample space and subset of sample space is considered as A. numerical complementary events. B. equal compulsory events c. complementary events. D. compulsory events | 12 |

1258 | In a sample survey of 640 people, it was found that 400 people have a secondary school certificate. If a person is selected at random, what is the probability that the person does not have such certificate? ( mathbf{A} cdot 0.375 ) B. 0.625 c. 0.725 D. 0.875 | 12 |

1259 | The given graph represent the how much consumers would be willing to pay for store brand and brand name products. If a consumer is chosen at random, then the probability that the consumer is will to pay at least ( $ 8 ) for the product is ( frac{u}{b}, ) where ( a, b ) are ( c 0 ) primes. Find the value of ( b-a ? ) Store Brand ( square ) Brand Name | 12 |

1260 | The random variable ( x ) follows normal distribution Then the value of ( C ) is A ( cdot sqrt{2 pi} ) в. ( frac{1}{sqrt{2 pi}} ) c. ( 5 sqrt{2 pi} ) D. ( frac{1}{5 sqrt{2 pi}} ) | 12 |

1261 | In the year 2009 , during rainy season of 90 days, it was observed that it rain to 20 days only. Find the probability that it did not rain. | 12 |

1262 | 6 married couples are standing in a room. If 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is? A ( cdot frac{16}{33} ) в. ( frac{8}{33} ) c. ( frac{17}{33} ) D. ( frac{24}{33} ) | 12 |

1263 | If ( A, B ) and ( C ) are mutually exclusive and exclusive events of a random experiment such that ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{2} boldsymbol{P}(boldsymbol{A}) ) and ( P(C)=frac{1}{2} P(B), ) then ( P(A cup C)= ) A ( cdot frac{10}{13} ) в. ( frac{3}{13} ) c. ( frac{6}{13} ) D. ( frac{7}{13} ) | 12 |

1264 | A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number ( 1,2,3, dots dots ., 12 ) as shown in figure. What is the probability that it will point to multiple of ( 4 ? ) ( A cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{4} ) D. E. None of these | 12 |

1265 | A die is thrown, write a sample space ( (S) ) and ( n(S) . ) If event ( A ) is getting a number greater than ( 4, ) write event ( A ) and ( n(A) ) | 12 |

1266 | A man alternatively tosses a coin and throws a die. The probability of getting a head on the coin before he gets 4 on the die is A ( cdot frac{6}{7} ) в. ( frac{2}{3} ) ( c cdot frac{3}{4} ) D. | 12 |

1267 | If two events ( A ) and ( B ) such that ( boldsymbol{P}left(boldsymbol{A}^{prime}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( boldsymbol{P}(boldsymbol{A} cap ) ( B)=0.3, ) then ( Pleft(B mid A cup B^{prime}right) ) is A . ( 3 / 8 ) B. 2 / c. ( 5 / 6 ) D. ( 1 / 4 ) | 12 |

1268 | From 7 gentlemen and 4 ladies, a committee of 5 is to be formed. The probability that this can be one so as to include at least one lady is A ( cdot frac{^{7} C_{5}}{^{11} C_{5}} ) в. ( frac{4}{^{11} C_{5}} ) ( ^{mathbf{C}} cdot_{1-frac{^{7} C_{5}}{11} C_{5}} ) D. ( _{1-frac{4}{11} C_{5}} ) | 12 |

1269 | In a simultaneous throw of a pair of dice, if the probability of getting a total of 9 or 11 is ( frac{1}{x} . ) Find ( x ) | 12 |

1270 | If ( C ) and ( D ) are two events such that ( C subset D ) and ( P(D) neq 0, ) then the correct statement among the following is ( mathbf{A} cdot P(C mid D)<P(C) ) ( ^{mathbf{B}} P(C mid D)=frac{P(D)}{P(C)} ) c. ( P(C mid D)=P(C) ) D. ( P(C mid D) geq P(C) ) | 12 |

1271 | A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is A ( cdot frac{3}{8} ) B. ( frac{1}{5} ) ( c cdot frac{3}{4} ) D. None of these | 12 |

1272 | An urn contains 6 white and 4 black balls. A fair die whose faces are numbered from 1 to 6 is rolled and number of balls equal to that of the number appearing on the die is drawn from the urn at random. The probability that all those are white is A. 1 5 B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) ( D cdot frac{4}{5} ) | 12 |

1273 | A fair die is rolled 180 times. The expected number of 6 is A . 50 B. 30 c. 10 D. | 12 |

1274 | Three bags contain 2 silver, 5 copper coins, and 3 silver, 4 copper coins and 5 silver, 2 copper coins respectively. A bag is chosen at random and a coin is drawn from it which happens to be silver. What is the probability that it has come from third bag? | 12 |

1275 | The mean score of 1000 students for an examination is 34 and standard deviation is 16 (i) How many candidates can be expected to obtain marks between 30 and 60 assuming the normality of the distribution and (ii) Determine the limits of the marks of the central ( 70 % ) of the candidates ( {P[0<z<0.25]=0.0987 ; P[0<z< ) 1.63 ( ]=mathbf{0 . 4 4 8 4} ; P[mathbf{0}<boldsymbol{z}<mathbf{1 . 0 4}]= ) ( mathbf{0 . 3 5}} ) | 12 |

1276 | In a class ( 5 % ) of boys and ( 10 % ) of girls have an I.Q of more than ( 150 . ) In this class ( 60 % ) of students are boys. If a student is selected at random and found to have an I.Q. of more than ( 150 . ) Find the probability that the student is a boy. A ( cdot frac{3}{7} ) B. ( frac{23}{7} ) ( c cdot frac{3}{5} ) D. None of these | 12 |

1277 | A discrete random variable ( X, ) can take all possible integer values from 1 to ( K ) each with a probability ( 1 / K . ) Its mean is ( mathbf{A} cdot K ) в. ( K+1 ) c. ( K / 2 ) D. ( K / 4 ) | 12 |

1278 | For any two events ( A ) and ( B ) in a sample space: This question has multiple correct options ( ^{mathbf{A}} cdot p(A / B) geq frac{P(A) P(B)-1}{P(B)} P(B) neq 0 ) is always true B ( cdot P(A cap bar{B})=P(A)-P(A cap B) ), does not hold ( mathbf{c} cdot P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( A ) and ( B ) are independent D ( cdot P(A cup B)=1=P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint. | 12 |

1279 | Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group. | 12 |

1280 | If ( A, B, C ) are three independent events of an experiment such that, ( boldsymbol{P}(boldsymbol{A} cap ) ( left.boldsymbol{B}^{C} cap boldsymbol{C}^{C}right)=frac{1}{4}, boldsymbol{P}left(boldsymbol{A}^{C} cap boldsymbol{B} cap boldsymbol{C}^{C}right)= ) ( frac{1}{8}, Pleft(A^{C} cap B^{C} cap C^{C}right)=frac{1}{4}, ) then find ( boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(boldsymbol{B}), boldsymbol{P}(boldsymbol{C}) ) | 12 |

1281 | An event in which all the possible outcomes of the experiments are present is known as event A. a complement. B. an experiment c. a sample space. D. an exhaustive event. | 12 |

1282 | Assertion Odd in favour of an event ( A ) are ( 2: 1 & ) odd in favour of ( A cup B ) are 3: 1 then ( frac{1}{12} leq P(B) leq frac{3}{4} ) Reason If ( boldsymbol{A} cap boldsymbol{B} subset boldsymbol{A} ) then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) leq boldsymbol{P}(boldsymbol{A}) ) A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true | 12 |

1283 | A bag contains 5 red balls and 8 blue balls. It also contains 4 green and 7 black balls. If a ball is drawn at random, then find the probability that it is not green A ( cdot frac{5}{6} ) B. ( frac{1}{4} ) ( c cdot frac{1}{6} ) D. ( frac{7}{4} ) | 12 |

1284 | An urn A contains 4 white and 6 redd balls. Three balls are drawn at random the expected number of white balls drawn is A . 3.0 B. 1.8 c. 1.2 D. 1. | 12 |

1285 | Events ( boldsymbol{A} ) and ( boldsymbol{B} ) are such that ( boldsymbol{P}(boldsymbol{A})= ) ( frac{1}{2}, P(B)=frac{7}{12} ) and ( P(text { not } A text { or } operatorname{not} B)=frac{1}{4} . ) State whether ( A ) and ( B ) are independent? A. True B. False | 12 |

1286 | A die is throw once. Find the probability of getting (1)an even number (2)a number less than 5 (3)a number greater than 2 (4)a number between 3 and 6 (5)a number other than 3 (6)the number 5 | 12 |

1287 | Suppose that two cards are drawn at random from a deck of cards. Let ( X ) be the number of aces obtained. Then the value of ( boldsymbol{E}(boldsymbol{X}) ) is A ( cdot frac{37}{221} ) в. ( frac{5}{13} ) c. ( frac{1}{13} ) D. ( frac{2}{13} ) | 12 |

1288 | Let ( A ) and ( B ) be two events such that ( boldsymbol{P}(overline{boldsymbol{A} cup boldsymbol{B}})=frac{1}{6}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{1}{4} ) and ( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for the complement of the event A. Then, the events ( A ) and ( B ) are A. Independent but not equally likely B. Independent and equally likely c. Mutually exclusive and independent D. Equally likely but not independent | 12 |

1289 | In a group of 400 people, 160 are smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are ( 35 %,, 20 % ) and ( 10 % ) respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is a smoker and non- vegetarian? | 12 |

1290 | If ( A ) and ( B ) are two events. The probability that at most one of ( A, B ) occurs is A ( .1-P(A cap B) ) в. ( P(bar{A})+P(bar{B})-P(bar{A} cap B) ) c. ( P(bar{A})+P(bar{B})+P(bar{A} cap bar{B}) ) D. All of the above | 12 |

1291 | Four cards are drawn from a deck of 52 cards, the probability of all being spade ¡s ( ^{A} cdot frac{1}{256} ) в. ( frac{1}{56} ) c. ( frac{1}{64} ) D. ( frac{31}{256} ) | 12 |

1292 | 16. Let É and F be two independent events. The probability that exactly one of them occurs is 11 and the probability of 25 none of them occurring is – fP(T) denotes the probability of occurrence of the event T, then (2011) (@) PLE)= ,PF)=} (6) PCE) = 5, PC)=} (C) PE)= 3, PCP)= (A) PLE)= 3, PCP)= | 12 |

1293 | According to the property of probability, the probability of an event cannot be A. greater than zero B. equal to zero c. less than zero D. equal to one | 12 |

1294 | If ( X ) follows a binomial distribution with parameters ( n=8 ) and ( P=frac{1}{2}, ) than ( boldsymbol{P}(|boldsymbol{x}-mathbf{4}| leq mathbf{2})= ) A ( cdot frac{119}{128} ) в. ( frac{9}{128} ) c. ( frac{101}{128} ) D. ( frac{11}{128} ) | 12 |

1295 | From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution. | 12 |

1296 | If the value of ( x ) is 6 A ( cdot frac{2}{3} ) B. ( frac{1}{3} ) ( c cdot frac{5}{6} ) D. | 12 |

1297 | There are two groups of subjects one of which consists of 5 science subjects and 3 engineering subjects and the other consists of 3 science and 5 engineering subjects. An unbaised die is cast. If number 3 or number 5 turns up, a subject is selected at random from the first group, other wise the subject is selected at random from the second group. Find the probability that an engineering subject is selected ultimately. A ( cdot frac{13}{24} ) B. ( frac{1}{3} ) ( c cdot frac{2}{3} ) D. ( frac{11}{24} ) | 12 |

1298 | The annual salaries of employees in a large company are approximately normally distributed with a mean of ( mathbf{5 0}, mathbf{0 0 0} ) and a standard deviation of ( 20,000 . ) What percent of people earn between 45,000 and ( 65,000 ? ) A . ( 56.23 % ) % B . ( 47.4 % ) c. ( 37.2 % ) D. 38.56% | 12 |

1299 | A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let ( A ) be the event, ‘the number is even’, and ( B ) be the event,’the number is red’. Then ( A ) and ( B ) are independent events. A. True B. False | 12 |

1300 | The largest possible variance of a binomial variate is A ( . n ) в. ( frac{n}{2} ) c. ( frac{n}{4} ) D. ( frac{n}{6} ) | 12 |

1301 | In a sequence of independent trials, the probability of success is ( 1 / 4 . ) If ( p ) denotes the probability that the second success occurs on the fourth trial or later trial, find ( 32 p ) | 12 |

1302 | In a horse race there are 18 horses numbered from 1 to 18. The probability that horse 1 would win is ( frac{1}{6}, ) horse 2 is ( frac{1}{10} ) and 3 is ( frac{1}{8} . ) Assuming a tie is impossible, the chance that one of the three horses wins the race, is A. ( frac{143}{420} ) B. ( frac{119}{120} ) C. ( frac{47}{120} ) D. ( frac{1}{5} ) | 12 |

1303 | Two fair dice are thrown. What is the probability that the two scores do not add to ( 5 ? ) ( A cdot frac{7}{9} ) в. ( frac{5}{9} ) ( c cdot frac{8}{9} ) D. ( frac{1}{9} ) | 12 |

1304 | A ball contains ( x ) white, ( y ) red, ( z ) blue balls. A ball is drawn at the random then, what is the probability of drawing blue ball. | 12 |

1305 | Let ( E_{1}, E_{2}, E_{3} dots E_{N} ) be the ‘n’ exhaustive events in a random experiment then ( boldsymbol{p}left(boldsymbol{E}_{1}right) boldsymbol{p}left(, boldsymbol{E}_{2}right), boldsymbol{p}left(boldsymbol{E}_{3}right) ldots boldsymbol{p}left(boldsymbol{E}_{N}right) ) is A. less than B. equal to c. greater than 1 D. none | 12 |

1306 | Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and another is red. | 12 |

1307 | There are 500 wrist watches in a box. Out of these 50 wrist watches are found defective. One watch is drawn randomly from the box. Find the probability that wrist watch chosen is a defective watch. | 12 |

1308 | The probability of getting number 10 in a throw of a dice is A. 0 B. ( c cdot 0.5 ) D. 0.75 | 12 |

1309 | When two dice are rolled : List the outcomes for the event that total is less than 5 . | 12 |

1310 | A die is thrown twice. Each time the number appearing on it is recorded. Describe the following event: ( B= ) Both numbers are even | 12 |

1311 | A medicine is known to be ( 75 % ) effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is curved by this medicine? A ( cdot frac{1}{1024} ) в. ( frac{243}{1024} ) c. ( frac{1023}{1024} ) D. ( frac{781}{1024} ) | 12 |

1312 | A die is thrown twice and the sum of the numbers appearing is observed to be 6 What is the conditional probability that the number 4 has appeared at least once? | 12 |

1313 | A coin is tossed 1000 times with the following frequencies: Head: ( 445, ) Tail: 555 When a coin is tossed at random, what is the probability of getting a tail? | 12 |

1314 | A fair coin is tossed four times. The probability that the tails exceed the heads in number is ( ^{mathbf{A}} cdot_{frac{4}{3} C}left(frac{1}{2}right)^{4} ) ( ^{mathbf{B}} cdot_{3}^{4} Cleft(frac{1}{2}right)^{4}+left(frac{1}{2}right)^{4} ) ( ^{c} cdotleft(frac{1}{2}right)^{4} ) ( ^{mathrm{D}} cdot_{3}^{4} Cleft(frac{1}{3}right)^{2}left(frac{2}{3}right)^{1} ) | 12 |

1315 | Рогдсо о стар, тоороо оо. For two given events A and B, P( A B) (1988 – 2 Marks) (a) not less than P (A)+P (B)-1 (b) not greater than P (A)+P(B) (c) equal to P (A) + P(B)-P (AUB) (d) equal to P (A) + P(B) + P (AUB) | 11 |

1316 | A die is thrown thrice. A success is 1 or 6 in a throw. If the sum of the mean and variance of the number of successes is ( frac{a}{3}, ) the value of a is | 12 |

1317 | Red on first draw and red on second draw | 12 |

1318 | Tossing a coin is an example of A. Infinite discrete sample space B. Finite sample space c. continuous sample space D. None of these | 12 |

1319 | Which one of the following is correct? A. An event having no sample point is called an elementary event B. An event having one sample point is called an elementary event C. An event having two sample point is called an elementary event D. An event having many sample point is called an elementary event | 12 |

1320 | If ( x ) is a random variable with probability distribution ( boldsymbol{p}(boldsymbol{x}=boldsymbol{k})= ) ( frac{(boldsymbol{k}+mathbf{1}) boldsymbol{C}}{mathbf{2}^{k}}, boldsymbol{k}=mathbf{0}, mathbf{1}, mathbf{2}, mathbf{3}, dots dots dots dots, ) then find ( C ) | 12 |

1321 | If ( A ) and ( B ) are events having probabilities, ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6 , P}(boldsymbol{B})= ) ( mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0}, ) then the probability that neither ( A ) nor ( B ) occurs is A ( cdot frac{1}{4} ) B. 1 ( c cdot frac{1}{2} ) ( D ) | 12 |

1322 | Rajnikant has 12 sketch pens and 8 fountain pens. He gave two of the pens to his brother. Find the probabilities of the following events using tree diagram i) Both the pens are sketch pens. ii) Only one is a sketch pen iii) Neither of them are sketch pens. | 12 |

1323 | If the variance of a random variable ( X ) is ( sigma^{2}, ) then the variance of the random variable X-5 is?? ( mathbf{A} cdot 5 sigma^{2} ) B . ( 25 sigma^{2} ) ( mathbf{c} cdot sigma^{2} ) D. ( 2 sigma^{2} ) | 12 |

1324 | A die is tossed twice. Find the probability of getting 4,5 or 6 on the toss and 1,2,3 or 4 on the second toss. | 12 |

1325 | A bag contains 4 white, 7 black and 5 green balls. What is the probability of picking white? | 12 |

1326 | A die is thrown. If ( A ) is the event that the number on upper face is an even, then write sample space and event ( boldsymbol{A} ) in set notation. | 12 |

1327 | Simone and her three friends were deciding how to pick the song they will ( operatorname{sing} ) for their school’s talent show. They decide to roll a number cube. The person with the lowest number chooses the song. If her friends rolled a ( 6,5, ) and ( 2, ) what is the probability that Simone will get to choose the song? A. ( frac{1}{6} ) B. c. 0 D. | 12 |

1328 | If two events ( A ) and ( B ) such that ( boldsymbol{P}left(boldsymbol{A}^{c}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap ) ( left.left.boldsymbol{B}^{c}right)=mathbf{0 . 5}, boldsymbol{P}left[boldsymbol{B} / boldsymbol{A} cup boldsymbol{B}^{c}right)right]=frac{1}{k}, ) then value of k is | 12 |

1329 | Suppose an integer from 1 through 100 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9 | 12 |

1330 | ( 102 A bag contains 4 blue, 5 red and 7 green balls. If a ball is drawn at random, what is the probability that it is blue? (a) 4/16 (b) 1/4 (c) 1/256 (d) 1/64 | 11 |

1331 | A family has two children. What is the probability that both the children are boys given that at least one of them is a boy? | 12 |

1332 | You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them type 1 ), 0.4 against a quarter of the players (call them type 2 ), and 0.5 against the remaining quarter of the players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning? A. 0.375 в. 0.986 ( c cdot 0.236 ) D. 0.135 | 12 |

1333 | The probability that at least one of the events ( A ) and ( B ) occurs is 0.7 and they occur simultaneously with probability ( 0.2 . ) Then ( P(bar{A})+P(bar{B})= ) A . 1.8 B. 0.6 c. ( 1 . ) D. 1. | 12 |

1334 | Two cards are drawn simultaneously from a well shuffled pack of 52 cards. The expected number of aces is A ( cdot frac{4}{13} ) в. ( frac{3}{13} ) c. ( frac{2}{13} ) D. ( frac{1}{13} ) | 12 |

1335 | The probability of event is 1 A. Sure B. Impossible c. exclusive D. mutually exclusive | 12 |

1336 | A bag contains 6 red, 4 white and 8 blue balls. If three ball are drawn at random, find the probability that: (i) All the three balls are red. (ii) All the three balls are blue. ( A ) (i) ( frac{5}{204}, ) (ii) ( frac{7}{102} ) в. (i) ( frac{9}{204}, ) (ii) ( frac{7}{102} ) ( c ) (i) ( frac{7}{204}, ) (ii) ( frac{5}{102} ) D. None of these | 12 |

1337 | ( Pleft(A / B^{prime}right) ) is defined only when ( A cdot B ) is not a sure event B. ( B ) is a sure event c. ( B ) is an impossible event D. ( B ) is not an impossible event | 12 |

1338 | If three dice are thrown, then the probability that they show the numbers in A.P.is A ( cdot frac{1}{36} ) в. ( frac{1}{18} ) ( c cdot frac{2}{9} ) D. ( frac{5}{18} ) | 12 |

1339 | 20. nts. 21. Let EC denote the complement of an event E. Let E, F, G be pairwise independent events with P(G) > 0 and P(EnFnG)=0. Then P(ECF|G) equals (2007-3 marks) (a) P(EC) + P(F) (b) P(EC) – P(F) (C) P(E)- P(F) (d) P(E)- P(F) | 12 |

1340 | ( operatorname{Let} boldsymbol{H}_{1}, boldsymbol{H}_{2}, boldsymbol{H}_{3}, dots, boldsymbol{H}_{n} ) be mutually exclusive and exhaustive events with ( boldsymbol{P}left(boldsymbol{H}_{i}right)>0 ; boldsymbol{i}=mathbf{1}, boldsymbol{2}, boldsymbol{3}, ldots, boldsymbol{n} . ) Let ( mathrm{E} ) be any other event with ( 0<P(E) ) ( boldsymbol{P}left(boldsymbol{E} mid boldsymbol{H}_{i}right) cdot boldsymbol{P}left(boldsymbol{H}_{i}right) ) for ( boldsymbol{i}=mathbf{1}, boldsymbol{2}, boldsymbol{3}, dots, boldsymbol{n} ) STATEMENT-2 ( sum_{i=1}^{n} Pleft(H_{i}right)=1 ) A. Statement-1 is True, Statement-2 is True; Statement – is a correct explanation for Statement- – B. Statement-1 is True, Statement-2 is True; Statement – is Not a correct explanation for Statement- 1 c. Statement- – – is True, Statement – 2 is False D. Statement-1 is False, Statement-2 is True | 12 |

1341 | Two coins are tossed, ( A ) is the event of getting at most one head, ( B ) is the event getting both heads, ( C ) is the event of getting same face on both the coins. The events ( A ) and ( B ) are: A. Mutually exhaustive B. Mutually exclusive c. same D. None of these | 12 |

1342 | A card is drawn from a deck of cards. What is the probability that it is either a spade or an ace or both A ( cdot frac{7}{13} ) в. ( frac{10}{13} ) c. ( frac{4}{13} ) D. ( frac{5}{13} ) | 12 |

1343 | A card from a pack of 52 cards is lost. from the remaining cards of pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond. | 12 |

1344 | In a group of 10 children, there are 6 boys and 4 girls, 3 children are selected at random. Find the probability that the selected group have only one special girl. | 12 |

1345 | One hundred identical coins, each with probability, ( p, ) of showing up heads are tossed once. If ( 0<p<1 ) and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of ( p ) is: ( A cdot frac{1}{2} ) в. ( frac{49}{101} ) c. ( frac{50}{101} ) D. ( frac{51}{101} ) | 12 |

1346 | The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of A King. | 12 |

1347 | A two-digit number is formed with the digits 2,5 and ( 7, ) where repetition of digits is not allowed. Find the probability that the number so formed is a square number | 12 |

1348 | An unbiased dice is tossed, The probability of getting a multiple of 3 is 1. 711f | 11 |

1349 | The probability that a man will be alive in 40 years is ( frac{3}{5}, ) and the probability that his wife will also survive 40 years is ( frac{2}{3} . ) Find the probability that both will be alive A B. ( frac{4}{5} ) ( c cdot frac{2}{15} ) D. ( frac{6}{15} ) | 12 |

1350 | There are n different objects, ( 1,2,3,4, ldots ) ( n, ) distributed at random in n places marked ( 1,2,3, ldots, ) n. If ( p ) is the probability that at least three of the objects occupy places corresponding to their number, find ( 6 p ) | 12 |

1351 | In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the selected person is female, is A ( cdot frac{2}{7} ) B. ( frac{1}{2} ) ( c cdot frac{1}{4} ) D. | 12 |

1352 | A card is thrown from a pack of 52 cards so that each cards equally likely to be selected. In which of the following cases are the events ( A ) and ( B ) independent? | 12 |

1353 | ( A, B, C ) are three mutually independent with probabilities 0.3,0.2 and 0.4 respectively. What is ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}) ? ) A. 0.400 B. 0.240 c. 0.024 D. 0.500 | 12 |

1354 | In a single throw of two dice, what is the probability of getting a total of 11. (a) 1/9 (6) 1/18 (c) 1/12 (d) 2/36 | 11 |

1355 | If ( frac{1+3 p}{3}, frac{1-p}{4} ) and ( frac{1-2 p}{2} ) are mutually exclusive events. Then, range of ( p ) is A ( cdot frac{1}{3} leq p leq frac{1}{2} ) в. ( frac{1}{2} leq p leq frac{1}{2} ) c. ( frac{1}{3} leq p leq frac{2}{3} ) D. ( frac{1}{3} leq p leq frac{2}{5} ) | 12 |

1356 | Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are ( frac{1}{4}, frac{1}{2} ) and ( frac{5}{8} ) respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? A ( cdot frac{11}{8} ) в. ( frac{7}{8} ) c. ( frac{9}{64} ) D. ( frac{5}{64} ) E ( cdot frac{3}{64} ) | 12 |

1357 | Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. Two balls are transferred at random from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred balls were both black | 12 |

1358 | The probability distribution function of a random variable ( boldsymbol{X} ) is given by : 0 1.2 ( boldsymbol{x}_{i} ) [ 10 c quad 5 c-1 ] ( 3 c ) where ( c>0 . ) Find ( c ) | 12 |

1359 | If ( A ) and ( B ) are two Mutually Exclusive events in a sample space S such that ( boldsymbol{P}(boldsymbol{B})=2 boldsymbol{P}(boldsymbol{A}) ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{S} ) then ( boldsymbol{P}(boldsymbol{A})= ) A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{4} ) D. 5 | 12 |

1360 | What is the probability that a leap year selected at random will contain 53 sundays? (6) 2 | 11 |

1361 | 9. A bag has 4 red balls and 2 yellow balls. (The balls are identical in all respects other than colour). A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball? Is it more or less than getting a yellow ball? | 11 |

1362 | A four-digit number is formed by using the digits 1,2,4,8 and 9 without repitition. If one number is selected from those numbers, then what is the probability that it will be an odd number ? A ( frac{1}{5} ) B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) D. ( overline{5} ) | 12 |

1363 | The probability of an event that is certain to happen is ( _{–}-_{-} ? ) A . 1 B. 2 ( c .3 ) ( D ) | 12 |

1364 | ( boldsymbol{8} boldsymbol{p}(boldsymbol{A} cap overline{boldsymbol{B}}) ) | 12 |

1365 | Three cards are drawn from a bag containing ( mathrm{m} ) cards marked ( 1,2,3 ldots . . n ) The probability that they form a sequence is A ( cdot frac{6}{n(n-1)} ) B. ( frac{3}{n(n-3)} ) c. ( frac{12}{n(n-2)} ) D. ( frac{3}{n(n-1)} ) | 12 |

1366 | UUес. 1. If M and N are any two events, the probability that exactly one of them occurs is (1984 – 3 Marks) (a) P(M)+ P(N) – 2P(M ON) (b) P(M) + P(N)-P(MON) (C) P(Mº)+ P(NC) -2P( M NC) (d) P(MONO)+P(M°ON) | 11 |

1367 | Three numbers are chosen at random withoutreplacement from the set of integers ( 1,2,3, ldots .10 . ) The probability that the minimum of thechosen numbers is 3 or the maximum of thechosen numbers is ( 7, ) is equal to A . ( 23 / 120 ) B. ( 13 / 120 ) c. ( 13 / 60 ) D. ( 11 / 40 ) | 12 |

1368 | Evaluate ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}), ) if ( boldsymbol{2} boldsymbol{P}(boldsymbol{A})= ) ( boldsymbol{P}(B)=frac{boldsymbol{5}}{13} ) and ( boldsymbol{P}(boldsymbol{A} / B)=frac{2}{5} ) | 12 |

1369 | The probability that a person will get an electric contract is ( frac{2}{5} ) and the probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) then the probability that he will get both is ( frac{17}{105} ) A. True B. False | 12 |

1370 | The blood groups of 30 students of Class VIII are recorded as follows: ( boldsymbol{A}, boldsymbol{B}, boldsymbol{O}, boldsymbol{O}, boldsymbol{A} boldsymbol{B}, boldsymbol{O}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O} ) ( boldsymbol{A}, boldsymbol{A B}, boldsymbol{O}, boldsymbol{A}, boldsymbol{A}, boldsymbol{O}, boldsymbol{O}, boldsymbol{A B}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A} ) Use this table to determine the probability that a student of this class, selected at random, has blood group ( A B ) | 12 |

1371 | Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is ( k(9 leq k leq 14) ) is ( ^{text {A } cdot} frac{21 k-k^{2}-83}{216} ) B. ( frac{k^{2}-3 k+2}{432} ) c. ( frac{21 k-k^{2}-83}{432} ) D. None of these | 12 |

1372 | appeared in a test of 100 marks in the subject of social studies and the data about the marks secured is as below: begin{tabular}{cc} Marks secured & Number of Students \ hline ( 0-25 ) & 50 \ ( 26-50 ) & 220 \ hline ( 51-75 ) & 100 \ Above 75 & 30 \ Total number of students & 400 \ hline end{tabular} If the result card of a student he picked up at random, what is the probability that the student has secured more than 50 marks. A. 0.586 B. 0.75 c. 0.325 D. 0.1 | 12 |

1373 | The experiment is to randomly select a human and measure his or her length. Identify the type of the sample space. A. Finite sample space B. Continuous sample space c. Infinite discrete sample space D. None of these | 12 |

1374 | An examination consists of 8 questions in each of which the candidate must say which one of the 5 alternatives is correct one. Assuming that the student has not prepared earlier choose for each of the question any one of 5 answer with equal probability. (i) Prove that the probability that he gets more than one correct answer is ( left(5^{8}-3 times 4^{8}right) / 5^{8} ) (ii) Find the probability that he gets correct answer to ( x ) or more questions. (iii) Find the standard deviation of this distribution. | 12 |

1375 | NOVI CSC. Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is (1980) (a) 0.39 (b) 0.25 (c) 0.11 (d) none of these | 11 |

1376 | An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that the most three of them are red is | 12 |

1377 | Three numbers are chosen at random withput replacement from ( {1,2, ldots, 15} ) Let ( E_{1} ) be the event that minimum of the chosen numbers is 5 and ( E_{2} ) their maximum is 10 then This question has multiple correct options ( ^{mathbf{A}} cdot Pleft(E_{1}right)=frac{9}{91} ) ( ^{mathrm{B}} cdot Pleft(E_{2}right)=frac{36}{455} ) ( ^{mathbf{C}} cdot Pleft(E_{1} cap E_{2}right)=frac{4}{455} ) ( Pleft(E_{1} mid E_{2}right)=frac{1}{9} ) | 12 |

1378 | If ( P(A cup B)=frac{3}{4} ) and ( P(bar{A})=frac{2}{3}, ) then find the value of ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) ) A ( cdot frac{3}{2} ) B. ( frac{1}{2} ) c. ( frac{5}{12} ) D. None of these | 12 |

1379 | In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear. A ( cdot frac{11}{36} ) в. ( frac{5}{18} ) c. ( frac{13}{18} ) D. ( frac{3}{16} ) | 12 |

1380 | A has 3 shares in a lottery in which there are 3 prizes and 6 blanks; ( B ) has 1 share in a lottery in which there is 1 prize and 2 blanks: show that ( A^{prime} s ) chance of success is to B’s as 16 to 7 | 12 |

1381 | For the three events ( A, B ) and ( C, P ) (exactly one of the events ( boldsymbol{A} ) or ( boldsymbol{B} ) occurs ( )=P(text { exactly one of the events } B ) or ( C text { occurs })=P( ) exactly one of the events ( C text { or } A text { occurs })=p ) and ( P( ) all the three events occur simultaneously) ( = ) ( p^{2}, ) where ( 0<p<1 / 2 . ) Then the probability of at least one of the three events ( A, B ) and ( C ) occurring is ( ^{mathrm{A}} cdot frac{3 p+2 p^{2}}{2} ) ( ^{text {В } cdot frac{p+3 p^{2}}{4}} ) c. ( frac{p+3 p^{2}}{2} ) ( frac{3 p+2 p^{2}}{4} ) | 12 |

1382 | From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king. A ( cdot frac{2}{52} ) в. ( frac{1}{52} ) c. ( frac{2}{13} ) D. ( frac{1}{26} ) | 12 |

1383 | If ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5 5}, boldsymbol{P}(boldsymbol{C})= ) ( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=boldsymbol{x}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})= ) ( mathbf{0 . 4 5}, boldsymbol{P}(boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap ) ( C)=0.2, ) then A. ( 0.2 leq x leq 0.45 ) в. ( 0.2 leq x leq 0.5 ) c. ( 0.2 leq x leq 0.65 ) D. ( 0.2 leq x leq 1 ) | 12 |

1384 | A biased coin is tossed twice.The probability of head is twice the tail.The PDF of number of heads is ( begin{array}{llll}mathbf{x} & mathbf{0} & mathbf{2} & mathbf{2}end{array} ) ( p(x) quad frac{a}{d} quad frac{b}{d} quad frac{c}{d} ) then values of ( a, b, c, d ) are A. ( a=1, b=2, c=3, d=4 ) В. ( a=1, b=4, c=4, d=9 ) c. ( a=1, b=4, c=4, d=10 ) D. ( a=1, b=2, c=1, d=4 ) | 12 |

1385 | Roll a fair die twice. Let ( A ) be the even that the sum of the two rolls equals six, and let ( B ) be the even that the same number comes up twice. What is ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ? ) A ( cdot frac{1}{6} ) в. ( frac{5}{6} ) ( c cdot frac{1}{5} ) D. none of these | 12 |

1386 | Which of the following is NOT a random experiment? A. Rolling an unbiased dice B. Tossing a fair coin c. Drawing a card from a well shuffled pack of 52 card D. None of these | 12 |

1387 | Opinion No. of students 135 dislike To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table. Find the probability that a student chosen at random (i) likes statistics (ii) does not like it. | 12 |

1388 | Which of the following is a correct statement about probability? A. It must have a value between -1 and 1 B. It is the collection of multiple experiments c. Result can be in the form of decimal or negative D. The probability of an event will not be less than 0 | 12 |

1389 | India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 1,2,3 are 0.45,0.05 and 0.50 respectively. Assuming that outcomes are independent, the probability of India getting at least 7 points is A .0 .0624 B. 0.0875 c. 0.8750 D. 0.0250 | 12 |

1390 | If the probability of defective bolts is ( 0.1, ) find the mean and standard deviation for the distribution of defective bolts in a total of 500 bolts. | 12 |

1391 | fin a binomial distribution the mean is 20, standard deviation is ( sqrt{15}, ) then ( p= ) A ( cdot frac{3}{4} ) B. ( frac{1}{4} ) ( c cdot frac{1}{2} ) D. | 12 |

1392 | If ( A ) and ( B ) are two mutually exclusive events then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= ) A. ( P(A) . P(B) ) в. ( P(A) ) c. 0 D. | 12 |

1393 | Consider the word ( W= ) MISSISSIPPI Number of ways in which the letters of the word ( W ) can be arranged if at least one vowel is separated from rest of the vowels A ( frac{8 ! .16 !}{4 ! 4 ! ! 2 !} ) в. ( frac{8 ! .16 !}{4.4 ! .2 !} ) c. ( frac{8 ! .16 !}{4 ! .2 !} ) D. ( frac{8 !}{4 ! .2 !} cdot frac{165}{4 !} ) | 12 |

1394 | Two events ( A ) and ( B ) are such that ( P(A)=frac{1}{4}, P(A mid B)=frac{1}{4} ) and ( P(B mid A)= ) ( mathbf{1} ) ( overline{2} ) Consider the following statements: (I) ( P(bar{A} mid bar{B})=frac{3}{4} ) (II) ( A ) and ( B ) are mutually exclusive ( (| I) P(A mid B)+P(A mid bar{B})=1 ) Then A. Only (I) is correct B. Only (I) and (II) are correct C. Only (I) and (III) are correct D. Only (II) and (III) are correct | 12 |

1395 | If ( A, B ) and ( C ) are mutually exclusive and exhaustive events, then ( boldsymbol{P}(boldsymbol{A})+ ) ( P(B)+P(C) ) equals to A ( cdot frac{1}{3} ) B. 1 ( c .0 ) D. Any value between 0 and 1 | 12 |

1396 | Sita and Geta are friends, what is the probability that both will have different birthdays (ignoring a leap year) A ( cdot frac{1}{365} ) в. ( frac{1}{364} ) c. ( frac{364}{365} ) D. None of these | 12 |

1397 | A fair die is thrown two times. Find the chance that Product of the numbers on the uppermost face is 12. | 12 |

1398 | Find the probability of successes in toss of a die, where a success is defined as (i) Number greater than 4 (ii) Six appears on die | 12 |

1399 | Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball drawn is white, what is the probability that the dice had turned up with a red face? | 12 |

1400 | A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 9 ( mathrm{km} / mathrm{hr} ) and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than ( 100 mathrm{km} / mathrm{hr} ? ) A .0 .1698 B. 0.1548 c. 0.1587 D. 0.1236 | 12 |

1401 | There are 4 white and 3 black balls in a box. In another box there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to ( 3, ) then a ball is drawn from the first box, but if it shows a number more than 3 , then a ball is drawn from the second box. If the ball drawn is black, then the probability that the ball was drawn from the first box is A ( cdot frac{1}{2} ) B. ( frac{6}{7} ) ( c cdot frac{4}{7} ) D. 3 7 | 12 |

1402 | If ( mathrm{M} ) and ( mathrm{N} ) are any two events, the probability that atleast one of them occurs is A ( cdot P(M)+P(N)-2 P(M cap N) ) B . ( P(M)+P(N)-P(M cap N) ) c. ( Pleft(M^{c}right)+Pleft(N^{c}right)-2 Pleft(M^{c} cap N^{c}right) ) D – ( Pleft(M cap N^{c}right)-Pleft(M^{c} cap Nright) ) | 12 |

1403 | Four cards are drawn at a time from a pack of 52 playing cards. Find the probability of getting all the 4 cards of the same suit. A ( cdot frac{44}{4165} ) В. ( frac{11}{4165} ) c. ( frac{22}{4165} ) D. none of these | 12 |

1404 | Choosing a queen from a deck of cards is an example of A. compound event B. complementary event c. simple event D. impossible event | 12 |

1405 | Two coins are tossed simultabeously. Find the probability of getting: (i) at least one Tail (ii) atmost two Head (iii) one Head | 12 |

1406 | If the integers ( m ) and ( n ) are chosen at random from 1 to 100 then the probability that ( 7^{m}+7^{n} ) is divisible by 5 is ( ? ) A. ( 1 / 5 ) B. 1/7 c. ( 1 / 4 ) D. 1/49 | 12 |

1407 | Suppose there are three urns containing 2 white and 3 black balls: 3 white and 2 black balls, and 4 white and one black ball respectively. There is equal probability of each urn being chosen. One ball is drawn from an urn chosen at random. The probability that a white ball is drawn is ( frac{k}{15} . ) Find the value of ( k ) | 12 |

1408 | A coin is tossed three times, where (i) ( E: ) head on third toss, ( F: ) heads on first two tosses (ii) ( E: ) at least tow heads, ( F: ) at most two heads (iii) ( E: ) at most two tails, ( F: ) at least one tail Determine ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) ) A. 0.42,0.50,0.85 В. 0.50,0.42,0.85 c. 0.85,0.42,0.30 D . .0.42, 0.46, 0.47 | 12 |

1409 | ( X ) has three children in his family. What is the probability that all the three children are boys? A ( cdot frac{1}{8} ) B. ( frac{1}{2} ) ( c cdot frac{1}{3} ) D. ( frac{3}{8} ) | 12 |

1410 | If ( A ) and ( B ) are two events such that ( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then ( ^{mathrm{A}} cdot P(A cup B) geq frac{3}{4} ) в. ( Pleft(A^{prime} cap Bright) leq frac{1}{4} ) c. ( frac{3}{8} leq P(A cap B) leq frac{5}{8} ) D. All of the above | 12 |

1411 | When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8 A ( cdot frac{1}{5} ) B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) D. None of these | 12 |

1412 | A biased coin (with probability of obtaining a Head equal to ( p>0 ) ) is tossed repeatedly and independently until the first head is observed. Compute the probability that the first head appears at an even numbered | 12 |

1413 | “The occurrence of one event excludes the occurrence of another event”. In a random experiment of probability theory, it is called A. Complementray event B. Impossible event c. Mutually exclusive event D. certain event | 12 |

1414 | Let ( boldsymbol{E}, boldsymbol{F}, boldsymbol{G} ) be pairwise independent events with ( P(G)>0 ) and ( P(E cap F cap ) ( G)=0 . ) Then ( Pleft(E^{prime} cap F^{prime} mid Gright) ) equals ( mathbf{A} cdot Pleft(E^{prime}right)+Pleft(F^{prime}right) ) B . ( Pleft(E^{prime}right)-Pleft(F^{prime}right) ) c. ( Pleft(E^{prime}right)-P(F) ) D. ( P(E)-Pleft(F^{prime}right) ) | 12 |

1415 | Given that ( boldsymbol{X} sim boldsymbol{B}(boldsymbol{n}=mathbf{1 0}, boldsymbol{p}) . ) If ( boldsymbol{E}(boldsymbol{X})=mathbf{8}, ) then the value of ( boldsymbol{p} ) is A . 0.6 в. 0.7 c. 0.8 D. 0.4 | 12 |

1416 | A man is know to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. the probability that it is actually a six is A ( cdot frac{3}{8} ) B. ( frac{1}{5} ) ( c cdot frac{3}{4} ) D. None of these | 12 |

1417 | Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings. | 12 |

1418 | A coin is tossed three times. Find ( P(A / B) ) in given cases: ( A= ) Heads on third tossed, ( B= ) Heads on first two tosses | 12 |

1419 | From 3 boys ( & 2 ) girls,commit a of 2 people is to be made. Then probability of minimum 1 boy in the committee is? | 12 |

1420 | ( X ) is a Normally distributed variable with mean ( =30 ) and standard deviation ( =4 . ) Find ( P(x>21) ) A . 0.9878 B. 0.9383 c. 0.9975 D. 0.9126 | 12 |

1421 | A box contains 32 coloured marbles. 8 of them are red marbles and the rest are either blue or green marbles. A marble is drawn at random. Calculate the probability of drawing a marble which is not red in colour. ( A cdot frac{2}{3} ) в. ( frac{5}{8} ) ( c cdot frac{3}{4} ) D. ( frac{7}{16} ) | 12 |

1422 | In a series of 3 one-day cricket matches between teams ( A ) and ( B ) of a college, the probability of team A winning or drawing are ( 1 / 3 ) and ( 1 / 6 ) respectively. If a win, loss or draw gives 2,0 and 1 point respectively, then what is the probability that team A will score 5 points in the series? A ( cdot frac{17}{18} ) B. ( frac{11}{12} ) ( c cdot frac{1}{12} ) D. ( frac{1}{18} ) | 12 |

1423 | If it rains a dealer in rain coats can earn Rs.500/- a day. If it is fair he will lose Rs. ( 40 /- ) a day. His mean profit if the probability of a fair day is 0.6 is: A. Rs. ( 230 /- ) B. Rs. ( 460 /- ) c. Rs. ( 176 /- ) D. Rs. 88/- | 12 |

1424 | A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point. A .0 .368 B. 0.147 c. 0.22 D. 0.073 | 12 |

1425 | Q Type your question Leagur Iuuchan a vaic, yuu unotive someone who is clearly supporting Manchester United in the game. What is the probability that they were actually born within 25 miles of Manchester? Assume that: ( Longrightarrow ) the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is ( frac{1}{20}, ) and ( Longrightarrow ) the chance that a person born within 25 miles of Manchester actually supports United is ( frac{7}{10} ) ( Longrightarrow ) the probability that a person not born within 25 miles of Manchester supports United with probability ( frac{1}{10} ) A ( cdot frac{7}{26} ) в. ( frac{8}{26} ) c. ( frac{9}{26} ) D. ( frac{10}{26} ) | 12 |

1426 | The probability for a randomly chosen month to have its ( 10^{t h} ) day as Sunday, is. A ( cdot frac{1}{84} ) в. ( frac{10}{12} ) c. ( frac{10}{84} ) D. | 12 |

1427 | The probability that a man hits a target is ( frac{3}{4} . ) If tried 5 time, the probability that he will hit the target at least three times,is A ( cdot frac{918}{10184} ) B. ( frac{884}{10244} ) c. ( frac{924}{1024} ) ( D cdot frac{848}{1024} ) | 12 |

1428 | A pair of dice is thrown 5 times. If getting a doublet is considered as a success, then find the mean and variance of successes. | 12 |

1429 | A policeman fires four bullets at a dacoit. The probability that the dacoit will be killed by one bullet is ( 0.6 . ) What is the probability that the dacoit is still alive? A .0 .064 B. 0.0256 c. 0.32 D. 0.16 | 12 |

1430 | Suppose that ( 5 % ) of men and ( 0.25 % ) of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male ? Assume that there are equal number of males and females. | 12 |

1431 | Suppose we throw a dice once? (i)What is the probability of getting a number greater than ( 4 ? ) | 12 |

1432 | LUDO In a test, the marks obtained by 15 students are 43, 73, 44, 93, 54, 64, 53, 24, 84, 40, 93, 33, 34, 74, 44. The probability that a pupil chosen at random passed the test, if the passing marks are 40 is (a) 8/15 (b) 4/5 (c) 7/15 (d) 48/60 d umhare from 1 to 1 | 11 |

1433 | An integer is chosen at random from the first 200 numbers.What is the probability that the integer chosen is divisible by 6 or 8. | 12 |

1434 | In a class of 100 students, 60 students drink tea, 50 students drink coffee and 30 students drink both. A student from class is selected at random, find the probability that student takes at least one of the two drinks (i.e. tea or coffee or both) ( A cdot 1 ) 5 B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) D. ( frac{4}{5} ) | 12 |

1435 | A random variable ( X ) has its range ( X= ) {3,2,1} with the probabilities, ( frac{1}{2}, frac{1}{3} ) and ( frac{1}{6} ) respectively. The mean value of ( X ) is A ( cdot frac{5}{3} ) B. ( frac{7}{3} ) ( c .3 ) ( D ) | 12 |

1436 | If ( A ) and ( B ) are events such that ( P(A)= ) ( frac{1}{2}, P(B)=frac{1}{3} ) and ( P(A cap B)=frac{1}{4}, ) then find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) | 12 |

1437 | In a bolt factory, machines ( A, B ) and ( C ) manufacture ( 25 %, 35 %, 40 % ) respectively. Of the total of their output ( 5 %, 4 % ) and ( 2 % ) are defective. A bolt is drawn and is found to be defective. What are the probabilities that it was manufactured by the machines ( A, B, C ) ( mathbf{A} cdot frac{25}{69}, frac{28}{69}, frac{16}{69} ) B. ( frac{28}{69}, frac{25}{69}, frac{16}{69} ) C ( cdot frac{25}{69}, frac{16}{69}, frac{28}{69} ) D. ( frac{16}{69}, frac{28}{69}, frac{25}{69} ) | 12 |

1438 | If two dice are rolled 12 times, obtain the mean and the variance of the distribution of successes, if getting a total greater than 4 is considered a success. | 12 |

1439 | An urn contains 25 balls of which 10 bear a mark ‘ ( X ) ‘ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark noted down and it is replaced. If 6 balls are drawn in this way, find the probability that (i) All will bear mark ‘ ( boldsymbol{X} ) (ii) Not more than two will bear ‘ ( Y ) ‘ mark | 12 |

1440 | Let ( S={1,2, ldots ., 20} . ) A subset ( B ) of ( S ) is said to be “nice”, if the sum of the elements of ( B ) is ( 203 . ) Then the probability that a randomly chosen subset of ( S ) is “nice” is: A ( cdot frac{6}{2^{20}} ) в. ( frac{5}{2^{20}} ) c. ( frac{4}{2^{20}} ) D. ( frac{7}{2^{20}} ) | 12 |

1441 | There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each? | 12 |

1442 | Two persons ( A ) and ( B ) are throwing an unbiased six faced die alternatively, with the condition that the person who throws 3 first wins the game. If ( A ) starts the game, the probabilities of ( A ) and ( B ) to win the same are respectively A ( cdot frac{6}{11}, frac{5}{11} ) в. ( frac{5}{11}, frac{6}{11} ) c. ( frac{8}{11}, frac{3}{11} ) D. ( frac{3}{11}, frac{8}{11} ) | 12 |

1443 | Given two mutually exclusive events ( boldsymbol{A} ) and ( B ) such that ( P(A)=frac{1}{2} ) and ( P(B)=frac{1}{3}, ) find ( P(A text { or } B) ) A ( cdot frac{3}{5} ) в. ( frac{5}{6} ) ( c cdot frac{4}{5} ) D. None of these | 12 |

1444 | Of the students in a college, it is known that ( 60 % ) reside in hostel and ( 40 % ) are day scholars.Previous year results report that ( 30 % ) of all students who reside in hostel attain ‘A’ grade and ( 20 % ) of day scholars attain ‘A’ grade in their annual examination. At the end of the year, one student is chose at random from the college and he has an ‘A’ grade, what is the probability that the student is a hostlier? | 12 |

1445 | For ( i=1,2,3,4 ) let ( T_{i} ) denote the event that the students ( S_{i} ) and ( S_{i+1} ) do NOT sit adjacent to each other on the day of the examination. Then the probability of the event ( boldsymbol{T}_{mathbf{1}} cap boldsymbol{T}_{mathbf{2}} cap boldsymbol{T}_{mathbf{3}} cap boldsymbol{T}_{mathbf{4}} ) is? A ( cdot frac{1}{15} ) в. ( frac{1}{10} ) c. ( frac{7}{60} ) D. | 12 |

1446 | A die is thrown. Write the sample space. If ( A ) is the event that the number is less than four, write the event ( boldsymbol{A} ) using set notation. | 12 |

1447 | f ( mathrm{E} ) and ( mathrm{F} ) are independent events then: This question has multiple correct options A. E & F mutually exclusive B. E & ( bar{F} ) (complement of the event ( F ) ) are independent C ( . bar{E} & bar{F} ) are independent D ( . P(E / F)+P(bar{E} / F)=1 ) | 12 |

1448 | Four letters mailed today each have a probability of arriving in two days or sooner equal to ( frac{2}{3} . ) Calculate the probability that exactly two of the four letters will arrive in two days or sooner. ( mathbf{A} cdot frac{4}{81} ) B. ( frac{16}{81} ) c. ( frac{6}{27} ) D. ( frac{8}{27} ) E ( cdot frac{4}{9} ) | 12 |

1449 | There are two balls in an urn whose colors are not known ( ball can be either white or black). A white ball is put into the urn. A ball is then drawn from the urn. The probability that it is white is A ( cdot frac{1}{4} ) B. ( frac{1}{3} ) ( c cdot frac{2}{3} ) D. | 12 |

1450 | What is called one or more outcomes of an experiment? A. Space B. Experiment c. sample D. Event | 12 |

1451 | Bag ( I ) contains 3 red and 4 black balls and Bag ( I I ) contains 4 red and 5 black balls. One ball is transferred from Bag ( boldsymbol{I} ) and Bag ( I I ) and then a ball is drawn from Bag ( I I . ) The ball so drawn is found to be red in colour. Find 310 times the probability that the transferred ball is black. | 12 |

1452 | An unbiassed die is toossed. Find the probability that it is a multiple of 3 | 12 |

1453 | ( A ) is known to speak truth 3 times out of 5 times. He throws a dice and reports that it is a one. Find the probability that it is actually one. | 12 |

1454 | A bag contains n white and n red balls. Pairs of balls are drawn without replacement until the bag is empty. Show that the probability that each pair consists of one white and one red ball is ( frac{mathbf{2}^{n}}{2 n} mathbf{C}_{n} ) | 12 |

1455 | If ( A ) and ( B ) are two mutually exclusive events, then This question has multiple correct options A ( . P(A) leq P(bar{B}) ) в. ( P(A)>P(B) ) c. ( P(B) leq P(bar{A}) ) ( D(A)<P(B) ) | 12 |

1456 | A bag contains 9 marbles, 3 of which are red, 3 of which are blue, and 3 of which are yellow. If three marbles are selected from the bag at random, what is probability that they are all of different colors? A ( cdot frac{1}{15} ) в. ( frac{9}{28} ) c. ( frac{1}{19} ) D. ( frac{1}{20} ) | 12 |

1457 | Two fair die are thrown. The probability the sum of the numbers appearing is 6 is A ( cdot frac{1}{6} ) в. ( frac{5}{6} ) c. ( frac{1}{36} ) D. ( frac{5}{36} ) | 12 |

1458 | The probability that a leap year not to contain 53 Sundays is. | 12 |

1459 | How many 4 -digit numbers can be formed from digit 1,1,2,2,3,3,4,4,5,5 ( ? ) | 12 |

1460 | Expected number of heads when we toss ( n ) unbiased coins is ( mathbf{A} cdot 2 n ) в. ( n ) ( c cdot frac{n}{2} ) D. ( frac{n}{4} ) | 12 |

1461 | A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. If the probability of the lost card is a diamond is ( boldsymbol{p} ) enter ( mathbf{1 0 0} boldsymbol{p} ) | 12 |

1462 | Given that ( A subset B, ) then identify the correct statement ( mathbf{A} cdot P(A / B)=P(A) ) B ( . P(A / B) leq P(A) ) ( mathbf{c} cdot P(A / B) geq P(A) ) D ( cdot P(A / B)=P(A)-P(B) ) | 12 |

1463 | The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then P(A) +P(B) is (1987-2 Marks) (a) 0.4 (6) 0.8 (c) 1. (d) 1.4 (e) none (Here A and B are complements of A and B, respectively). | 11 |

1464 | Four persons can hit a target correctly with probabilities ( frac{1}{2}, frac{1}{3}, frac{1}{4} ) and ( frac{1}{8} ) respectively. If all hit at the target independently, then the probability that the target would be hit, is? A ( cdot frac{25}{192} ) в. ( frac{1}{192} ) c. ( frac{25}{32} ) D. ( frac{7}{32} ) | 12 |

1465 | Probability of hitting a target independently of 4 persons are ( frac{1}{2}, frac{1}{3}, frac{1}{4}, frac{1}{8} . ) Then the probability that target is hit, is? A ( cdot frac{1}{192} ) в. ( frac{5}{192} ) c. ( frac{25}{32} ) D. ( frac{7}{32} ) | 12 |

1466 | For any two events ( A ) and ( B ), the conditional probability ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})= ) ( frac{P(B cap A)}{P(A)} ) and ifAand ( B ) are independent ( boldsymbol{P}(boldsymbol{B} cap boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) cdot boldsymbol{P}(boldsymbol{A}) ) So, ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) ) A lot contains 50 defective and 50 non- defective bulbs. Two bulbs are drawn at random one at a time with replacement. The events ( A, B, C ) are defined as: ( mathbf{A}: ) 1st bulb is defective ( mathrm{B}: ) 2nd bulb is non-defective ( mathrm{C}: ) both are defective or both are non- defective then, A. A, B, C are pair-wise independent as well as mutually independent B. A, B, C are pair-wise independent but mutually not c. ( A, B, C ) are mutually independent but pair-wise not D – of these | 12 |

1467 | Three coins are tossed describe (i) Two events which are mutually exclusive (ii) Three events which are mutually exclusive and exhaustive (iii) Two events which are not mutually exclusive (iv) Two events which are mutually exclusive but not exhaustive (v) Three events which are mutually exclusive but not exhaustive | 12 |

1468 | A fair coin is tossed at a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is A ( cdot frac{1}{64} ) в. ( frac{1}{32} ) c. ( frac{1}{16} ) D. | 12 |

1469 | If ( A ) and ( B ) are independent events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, ) find ( P(B) ) | 12 |

1470 | Suppose that of all used cars of a particular year ( 30 % ) have bad brakes. You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked. The chance that the mechanic will give you the wrong report is ( 20 % ). Assuming that the car you take to the mechanic is selected at random from the population of cars of that year. The chance that the car’s brakes are good, given that the mechanic says its brakes are good, is A ( frac{28}{130} ) в. ( frac{29}{31} ) c. ( frac{37}{62} ) D. ( frac{29}{62} ) | 12 |

1471 | What is the probability of getting a king if a card is drawn from a pack of 52 cards? A ( cdot frac{1}{52} ) в. ( frac{2}{52} ) c. ( frac{3}{52} ) D. ( frac{4}{52} ) | 12 |

1472 | Rahim takes out all the hearts from the cards. What is the probability of Picking out an ace from the remaining pack. | 12 |

1473 | he horses a Kr. A seleder Five horses are in a race. Mr. A selects two of the home random and bets on them. The probability that Mr. A sel the winning horse is 12003 | 11 |

1474 | P 11. Sol. Total number of outcomes 25 Find the probability of getting a number less than 5 in a single throw of an Total number of outcomes = 6 | 11 |

1475 | A bag contains 4 balls.Two balls drawn at random without replacement and are found to be white. What is the probability that all balls are white? | 12 |

1476 | A sum of money is rounded off to the nearest rupee. The probability that the round off error is at least ten paisa is ( frac{9 k}{100} . ) The value of ( k ) is | 12 |

1477 | A box contain ( N ) coins, ( m ) of which are fair and rest are biased. The probability of getting a head when a fair coin is tossed is ( frac{1}{2}, ) while it is ( frac{2}{3} . ) when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is A ( cdot frac{8 mathrm{m}}{8 mathrm{N}+mathrm{m}} ) B. ( frac{mathrm{m}}{8 mathrm{N}+mathrm{m}} ) c. ( frac{9 mathrm{m}}{8 mathrm{N}+mathrm{m}} ) D. ( frac{9 mathrm{N}}{8 mathrm{N}+mathrm{m}} ) | 12 |

1478 | A coin is tossed 3 times, the total number of possible outcomes is: A . 3 B. 4 ( c .6 ) ( D ) | 12 |

1479 | To define probability disribution function we assign to each variable A. the respective probabilities B. the specific random values c. some integers D. none | 12 |

1480 | Suppose that the letter cards for the word ( M ) ATHEMATICS were putt face down and mixed up and a card is picked up at random. What is the probability of picking up a vowel? | 12 |

1481 | A biased coin with probability ( P,(0<p< ) 1) of heads is tossed until a head appear for the first time. If the probability that the number of tosses required is even is ( frac{2}{5} ) then ( P= ) ( A cdot frac{2}{5} ) B. ( c cdot frac{1}{3} ) ( D cdot frac{3}{5} ) | 12 |

1482 | A card is drawn from the pack of 25 cards labelled with numbers 1 to 25 Write the sample space for this random experiment. | 12 |

1483 | The probability of an ordinary year having 53 Tuesdays is: A ( cdot frac{2}{7} ) B. ( frac{1}{7} ) ( c cdot frac{3}{7} ) D. | 12 |

1484 | A die is thrown once. What is the probability of getting a number less than ( 3 ? ) | 12 |

1485 | At random all the letters of the word “ARTICLE” are arranged in all possible ways. The probability that the arrangement begins with vowel and ends with a consonant is A . ( 1 / 7 ) в. ( 2 / 7 ) c. ( 3 / 7 ) D. ( 4 / 7 ) | 12 |

1486 | A company has two plants to manufacture televisions. The plant manufacture ( 70 % ) of televisions and plant II manufacture ( 30 % . ) At plant 1,80 ( % ) of the televisions are rated as of standard quality and at plant II, ( 90 % ) of the televisions are rated as of standard quality. A television is chosen at random and is found to be of standard quality. The probability that it has come from plant II is | 12 |

1487 | An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss then a die is rolled once. Find the sample space | 12 |

1488 | If ( A ) and ( B ) are mutually exclusive such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} ) find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) | 12 |

1489 | The probability that a student selected at random from a class will pass in Mathematics is ( 4 / 5, ) and the probability that he/she passes in Mathematics and Computer Science is ( 1 / 2 . ) What is the probability that he/she will pass in Computer Science if it is known that he has passed in Mathematics? | 12 |

1490 | Probability ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{B})= ) ( mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3}, ) then ( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right) ) is equal to A . ( 0 . ) в. 0.3 ( c .0 .2 ) D. 0.4 | 12 |

1491 | For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours. A .0 .4082 B. 0.4025 c. 0.4213 D. 0.4156 | 12 |

1492 | What is ( P(Z=10) ) equal to ( ? ) ( mathbf{A} cdot mathbf{0} ) в. ( 1 / 2 ) c. ( 1 / 3 ) D. ( 1 / 5 ) | 12 |

1493 | 7. E and F are two independent events. The probability that Don E and Fhappen is 1/12 and the probability that neither Enor F happens is 1/2. Then, (1993 – 2 Marks) (a) P(E)=1/3,P(F)=1/4 (b) P(E)=1/2,P(F)=1/6 (c) P(E)=1/6, P(F)= 1/2 (d) P(E)=1/4, P(F)=1/3 | 12 |

1494 | A bag contains 10 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green that a second year student is chosen. | 12 |

1495 | A coin is tossed until a head appears or it has been tossed 3 times. Given that head does not appear on the first toss, the probability that the coin is tossed 3 times is A ( cdot frac{1}{4} ) B. ( frac{3}{8} ) ( c cdot frac{1}{8} ) D. | 12 |

1496 | A biased coin with probability ( boldsymbol{p}, boldsymbol{0}< ) ( p<1, ) of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is ( 2 / 5, ) then ( p=dots ) A. ( 2 / 5 ) B. ( 2 / 3 ) c. ( 1 / 3 ) D. ( 3 / 5 ) | 12 |

1497 | A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table show the result of 1000 cases : Distance in ( K m quad ) Frequency Less than 4000 20 4000 to 9000 210 9000 to 14000 325 More than 14000 445 If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between ( 4000 mathrm{km} ) and ( 14000 mathrm{km} ) ? A . 0.65 B. 0.625 c. 0.125 D. None of these | 12 |

1498 | If ( A, B ) be two events such that ( P(A cup ) ( B)=frac{5}{6}, P(A cap B)=frac{1}{3} ) and ( Pleft(B^{prime}right)=frac{1}{2} ) then events ( A, B ) are A. dependent B. independent c. mutually exclusive D. none of these | 12 |

1499 | If 3 coins are tossed simultaneously, the probability of 2 heads and 1 tail is: A ( cdot frac{5}{8} ) B. ( frac{1}{8} ) ( c cdot frac{3}{8} ) D. ( frac{7}{8} ) | 12 |

1500 | If ( boldsymbol{P}left(boldsymbol{E}_{boldsymbol{k}}right) propto boldsymbol{k} ) for ( boldsymbol{0} leq boldsymbol{k} leq boldsymbol{n}, ) then ( lim _{n rightarrow infty} sum_{k=0}^{n} Pleft(E_{k} mid Aright) ) equals ( mathbf{A} cdot mathbf{0} ) B. ( 1 / 2 ) c. ( 1 / 6 ) ( D ) | 12 |

1501 | Three cards are drawn at random from a pack of 52 cards. What is the probability that all the three cards are kings? | 12 |

1502 | A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor queen? | 12 |

1503 | Probability of getting 2 when we roll a dice | 12 |

1504 | One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9 black balls. One ball is taken from each bag. What is the probability that both the balls will be of the same colour? A ( cdot 207 / 625 ) B. ( 191 / 625 ) c. ( 23 / 625 ) D. ( 227 / 625 ) | 12 |

1505 | Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are: (a) Mutually exclusive (1979) (6) Independent and mutually exclusive (c) Dependent | 12 |

1506 | A packet of 10 CD’s contains 4 defected. The CD’s are selected at random, one by one, examined and are not replaced. The probability that 7 th ( C D ) is the last defective is A ( cdot frac{2}{21} ) B. ( frac{4}{9} ) c. ( frac{7}{27} ) D. None of these | 12 |

1507 | ( A ) and ( B ) are two independent events. The probability that both ( A ) and ( B ) occur is ( frac{1}{6} ) and the probability that neither of them occur is ( frac{1}{3} ). Then ( P(A) ) is equal to A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{5}{6} ) D. ( frac{1}{2} ) or ( frac{1}{3} ) | 12 |

1508 | If ( A ) and ( B ) are two events, such that ( P(A ) or ( mathrm{B} ) ) ( =mathrm{P}(mathrm{A}), ) then A. events A and B are mutually exclusive B. events A and B are statistically independent c. event B is a subset of event A D. event A is a subset of event B | 12 |

1509 | 8. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of (1) getting a number 6? (i) getting a number less than 6? (iii) getting a number greater than 6? (iv) getting a 1-digit number? | 11 |

1510 | For any two events ( A ) and ( B ) This question has multiple correct options ( mathbf{A} cdot P(A cap B) geq P(A)+P(B)-1 ) B ( cdot P(A cap B) geq P(A)+P(B) ) ( mathbf{c} cdot P(A cap B)=P(A)+P(B)-P(A cup B) ) D ( cdot P(A cap B)=P(A)+P(B)+P(A cup B) ) | 12 |

1511 | A fair die is thrown. What is the probability that the score is not a factor of 5? A ( cdot frac{1}{5} ) B. ( frac{1}{3} ) ( c cdot frac{5}{6} ) D. ( frac{2}{3} ) | 12 |

1512 | 4 cards are chosen from a pack of 52 playing cards? In how many of these two are red cards and two are black cards. | 12 |

1513 | A problem in mathematics is given to the in mathematics is given to three students A, B, C their respective probability of solving the problem is 1. 1 1 is and Probability that the problem is solved is [2002] | 12 |

1514 | The probability of guessing the correct answer to a certain questions is ( frac{x}{2} . ) the probability of not guessing the correct answer is ( frac{3 x}{2}, ) then find the value of ( x ) | 12 |

1515 | Sample space for experiment in which a dice is rolled is A . 4 B. 8 c. 12 D. None of these | 12 |

1516 | Two probability distributions of the discrete random variable ( X ) and ( Y ) are given below. ( boldsymbol{X} quad mathbf{0} ) 3 ( mathbf{2} ) ( P(X) quad frac{1}{5} quad frac{2}{5} quad frac{1}{5} quad frac{1}{5} ) [ begin{array}{ccccc} boldsymbol{Y} & mathbf{0} & mathbf{1} & mathbf{2} & mathbf{3} \ P(Y) & frac{1}{5} & frac{3}{10} & frac{2}{5} & frac{1}{10} end{array} ] Then A. [ Eleft(Y^{2}right)=2 E(X) ] B. [ Eleft(Y^{2}right)=E(X) ] ( mathbf{c} cdot E(Y)=E(X) ) ( D ) [ Eleft(X^{2}right)=2 E(Y) ] | 12 |

1517 | If we throw a dice, then the sample space, ( S=1,2,3,4,5,6 . ) Now the event of 3 appearing on the dice is simple and given by A. ( E=2,3 ) В. ( E=1,2,3 ) c. ( E=3 ) D. ( E=1,3 ) | 12 |

1518 | A fair coin is tossed ( 2 n ) times. The probability of getting as many heads in the first ( n ) tosses as in the last ( n ) is A ( cdot frac{2 n_{C_{n}}}{2^{2 n}} ) B. ( frac{2 n_{C_{n-1}}}{2^{n}} ) c. ( frac{n}{2^{n}} ) D. ( frac{n^{2}}{2^{n}} ) | 12 |

1519 | A coin is tossed 100 times and tail is obtained 10 times. Now, if a coin is tossed at random, what is the probability of getting a head? A ( cdot frac{11}{10} ) в. ( frac{9}{10} ) c. ( frac{90}{10} ) D. ( frac{100}{10} ) | 12 |

1520 | ( A ) has 3 tickets of a lottery containing 3 prizes and 9 blanks. ( B ) has two tickets of another lottery containing 2 prizes and 6 blanks. The ratio of their chances of success is A ( cdot frac{32}{55}: frac{15}{28} ) в. ( frac{32}{55}: frac{13}{28} ) c. ( frac{34}{55}: frac{13}{28} ) D. ( frac{34}{55}: frac{15}{28} ) | 12 |

1521 | An experiment succeeds twice as often as it fails. Find the chance that in the next six trials, there shall be at least four successes. A ( cdot frac{233}{729} ) в. ( frac{64}{729} ) c. ( frac{496}{729} ) D. ( frac{432}{729} ) | 12 |

1522 | If A, B are two independent events, ( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= ) A ( cdot frac{3}{32} ) в. ( frac{29}{32} ) c. ( frac{15}{32} ) D. ( frac{5}{32} ) | 12 |

1523 | 19. One ticket is selected at random from 50 tickets numbered 00,01.02…., 49. Then the probability that the sum of the digits on the selected ticket is given that the product of these digits is zero, oquals: (2009) | 12 |

1524 | Die ( A ) has 4 red and 2 white faces whereas die ( B ) has 2 red and 4 white faces. A coin is flipped once. If it shows a head, the game continues by throwing die ( A, ) if it shows tail, then die ( B ) is to be used. If the probability that die ( A ) is used is ( frac{64}{66} ) where it is given that red turns up every time in first ( n ) throws, then ( n ) is | 12 |

1525 | The contents of three bags ( I, I I ) and ( I I I ) are as follows: Bag ( I: 1 ) white, 2 black 3 red balls Bag ( I I: 2 ) white, 1 black 1 red balls Bag III : 4 white, 5 black 3 red balls A bag is chosen at random and two balls are drawn. What is the probability that the balls are white and red | 12 |

1526 | A coin is tossed two times, what is the probability of getting head at least once | 12 |

1527 | Sixteen players ( boldsymbol{S}_{1}, boldsymbol{S}_{2}, ldots . boldsymbol{S}_{16} ) play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. The probability that the player ( S_{1} ) is among the eight winners is ( frac{1}{k} . ) Find the value of ( boldsymbol{k} ) | 12 |

1528 | From a lot of 30 bulbs which include 6 defectives, a sample of 2 bulbs are drawn at random with replacement. Find the probability distribution of the number of defective bulbs. | 12 |

1529 | Out of following which are random variables This question has multiple correct options A. ( x= ) “Number of heads when two coins are tossed B. ( x= ) “Sum of digits on uppermost face of two dice c. solution of ” ( X-4=0 ” ) D. ( x= ) “Raining | 12 |

1530 | Let ( A ) and ( B ) be two events such that ( P(overline{A cup B})=frac{1}{6}, P(A cap B)=frac{1}{4} ) and ( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for complement of event ( A ). Then, the events ( A ) and ( B ) are A. Mutually exclusive and independent B. Independent, but not equally likely c. Equally likely but not independent D. Equally likely and mutually exclusive | 12 |

1531 | The probability that at least one of the events ( A ) and ( B ) occur is ( 0.6 . ) If ( A ) and ( B ) occur simultaneously with probability 0.2, then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= ) A . 0.4 B. 0.8 c. 1.2 D. 1. | 12 |

1532 | A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white. | 12 |

1533 | 11. There are four machines and it is known that exactly two 01 them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is (1998 – 2 Marks) (a) 13 (6) 1/6 (c) 1/2 (d) 1/4 | 12 |

1534 | A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white. | 12 |

1535 | A and B play a game in which ( mathbf{A}^{prime} ) s chance of winning is ( frac{1}{5} ) in a series of 6 games, the probability that A will win all the 6 games is ( ^{mathrm{A}} cdot_{frac{6}{2} C}left(frac{1}{5}right)^{6} ) ( ^{mathrm{B}} cdot_{6}^{6} Cleft(frac{1}{5}right)^{6}left(frac{4}{5}right)^{0} ) ( ^{mathbf{C}} cdotleft(frac{4}{5}right)^{6} ) ( ^{mathrm{D} cdot}_{^{6}} Cleft(frac{1}{5}right)^{5}left(frac{4}{5}right) ) | 12 |

1536 | The probability that at least one of the events ( A ) and ( B ) occurs is ( 0.6, ) If ( A ) and ( B ) occur simultaneously with probability 0.2, then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}}) ) is A. 0.4 B. 0.8 ( c cdot 1.2 ) D. 1.4 | 12 |

1537 | There are 100 tickets in a raffle (Lottery). There is 1 prize each of Rs. ( mathbf{1 0 0 0} /-, ) Rs. ( mathbf{5 0 0} /- ) and Rs. ( mathbf{2 0 0} /- ) Remaining tickets are blank. Find the expected price of one such ticket. | 12 |

1538 | ( A ) and ( B ) alternately cut a pack of cards which is shuffled after each cut. The game is started by ( A ) and continuous until one of the players cuts a club. The probability that ( B ) win the game is ( k / 7 ) Find ( k ) | 12 |

1539 | A random variable ‘ ( X ) ‘ has the following probability distribution: [ begin{array}{lcccc} x=x & 0 & 1 & 2 & 3 \ P(X=x) & 0 & k & 2 k & 2 k end{array} ] Find: (i) ( k ) (ii) The Mean and (iii) ( boldsymbol{P}(boldsymbol{0}<boldsymbol{X}<mathbf{5}) ) | 12 |

1540 | Cards of an ordinary deck of playing cards are placed into two heaps. Heapconsists of all the red cards and heap-II consists of all the black cards. A heap is chosen at random and a card is drawn, find the probability that the card drawn is a king. | 12 |

1541 | Identify which number cannot be a probability? This question has multiple correct options A . ( 0 . ) B . -0.45 c. 1 D. 1. | 12 |

1542 | In a building programme the event that all the materials will be delivered at the correct time is ( M ) and the event that the building programme will be completed on time is ( F . ) Given that ( boldsymbol{P}(M)=mathbf{0 . 8} ) and ( boldsymbol{P}(boldsymbol{M} cap boldsymbol{F})=mathbf{0 . 6 5} ) find ( boldsymbol{P}(boldsymbol{F} / boldsymbol{M}) . ) If ( boldsymbol{P}(boldsymbol{F})=mathbf{0 . 7}, ) find the probability that the building programme will be completed on time if all the materials are not delivered at the correct time. ( ^{mathbf{A}} cdot P(F / M)=frac{11}{16} ; P(F / bar{M})=frac{1}{6} ) B. ( P(F / M)=frac{15}{16} ; P(F / bar{M})=frac{1}{8} ) ( ^{mathbf{c}} cdot P(F / M)=frac{13}{16} ; P(F / bar{M})=frac{1}{4} ) D. None of these | 12 |

1543 | Let ( A ) and ( B ) be two events such that ( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right)=mathbf{0 . 2 0}, boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}right)=mathbf{0 . 1 5} ) ( P(A text { and } B text { both fail })=0.10 . ) Then This question has multiple correct options A. ( P(A / B)=11 / 14 ) В . ( P(A)=0.7 ) c. ( P(A cup B)=0.9 ) D. ( P(A / B)=1 / 2 ) | 12 |

1544 | Let ( A ) and ( B ) be two finite sets having ( m ) and ( n ) elements respectively such that ( boldsymbol{m} leq boldsymbol{n} . ) A mapping is selected at random from the set of all mappings from ( A ) to ( B ). The probability that the mapping selected is an injection, is A. ( frac{n !}{(n-m) ! m^{n}} ) в. ( frac{n !}{(n-m) ! n^{m}} ) c. ( frac{m !}{(n-m) ! n^{m}} ) D. ( frac{m !}{(n-m) ! m^{n}} ) | 12 |

1545 | Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both balls are red, | 12 |

1546 | An ( M B M ) applies for a job in two firms ( X ) and ( Y . ) The probability of his being selected in firm ( X ) is 0.7 and being rejected at ( Y ) is ( 0.5 . ) The probability of at least one of his applications being rejected is ( 0.6 . ) The probability that he will be selected in one of the firms, is A . 0.6 B. 0.4 ( c .0 .8 ) D. None of these | 12 |

1547 | Suppose ( X ) has a binomial distribution ( B ) of ( 6, frac{1}{2} . ) Show that ( X=3 ) is the most likely outcome (Hint ( : P(X=3) ) is the maximum among all ( left.boldsymbol{P}left(boldsymbol{x}_{i}right), boldsymbol{x}_{i}=mathbf{0}, mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, boldsymbol{6}right) ) | 12 |

1548 | In a construction job, following are some probabilities given: Probability that there will be strike is ( 0.65, ) probability that the job will be completed on time if there is no strike is ( 0.80, ) probability that the job will be completed on time if there is strike is 0.32. Determine probability that the construction job will get complete on time A .0 .438 в. 0.538 ( c cdot 0.488 ) D. None of these | 12 |

1549 | In an examination hall there are four rows of chairs. Each row has 8 chairs one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that in each row, all students belong to the same class and that no two adjacent rows are allotted to the same class. In how many ways can these 32 students be seated? | 12 |

1550 | The below frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group ( A B ) Blood group Number of students ( A ) 9 ( B ) 6 th 3 12 Total 30 | 12 |

1551 | If ( A ) and ( B ) be two events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} ) ( B)=0.6, ) then value of ( Pleft(frac{bar{A}}{B}right)+ ) ( Pleft(frac{A}{bar{B}}right) ) is ( A ) в. ( frac{3}{4} ) ( c cdot frac{2}{5} ) D. ( frac{13}{12} ) E. ( frac{11}{12} ) | 12 |

1552 | In a simultaneous throw of a pair of dice, if the probability of getting odd number on the first and 6 on the second is ( frac{1}{a} . ) Find ( a ) | 12 |

1553 | In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas. A . 10 B . 15 c. 20 D. 25 | 12 |

1554 | ( A ) and ( B ) are two independent events of an experiment .if ( boldsymbol{P}(boldsymbol{n} boldsymbol{o} boldsymbol{t} boldsymbol{B})= ) ( mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 8 5}, ) find ( boldsymbol{P}(boldsymbol{A}) ) | 12 |

1555 | ( A ) and ( B ) are two independent witnesses is a case. The probability that ( A ) will speak truth is ( x ) and the probability that ( B ) will speak the truth is ( y . A ) and ( B ) agree in a certain statement. The probability that the statement is true is A ( cdot frac{x y}{1-x y} ) в. ( frac{x y}{1-x-y+2 x y} ) c. ( frac{2 x y}{x-y} ) D. ( frac{x y}{1-x-y} ) | 12 |

1556 | n an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons ( A, B ) and ( C ) carries out this task. ( A ) has ( 45 % ) chance, ( B ) has ( 35 % ) chance and ( C ) has ( 20 % ) chance of doing the task. The probability that ( A, B ) and ( C ) will take more than the allotted time is ( frac{1}{6}, frac{1}{10} ) and ( frac{1}{20} ) respectively. If it is found that the time taken is more than the allotted time, what is the probability that ( A ) has done the task? | 12 |

1557 | If ( C ) and ( D ) are two events such that ( mathbf{C} subset mathbf{D} ) and ( mathbf{P}(mathbf{D}) neq mathbf{0}, ) then the correct statement among the following is ( ^{mathbf{A}} cdot pleft(frac{C}{D}right)=mathrm{P}(mathrm{C}) ) ( ^{mathbf{B}} cdot pleft(frac{C}{D}right) geq mathrm{P}(mathrm{C}) ) ( ^{c} cdot pleft(frac{C}{D}right)<mathrm{P}(mathrm{C}) ) ( Pleft(frac{C}{D}right)=frac{P(D)}{P(C)} ) | 12 |

1558 | Given find ( boldsymbol{P}(boldsymbol{A})=frac{1}{5}, ) find ( boldsymbol{P}(boldsymbol{A} text { or } boldsymbol{B}), ) if ( A ) and ( B ) are mutually exclusive events. | 12 |

1559 | On one page of a telephone directly, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example in the number 25828573 the unit place digit is 3 ) is given in table below : Digit Frequency 22 26 22 22 Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is more than ( 7 ? ) ( A ) [ 0.15 ] в. 0.17 ( c ) 0.18 D. None of these | 12 |

1560 | Three groups ( A, B, C ) are contesting for positions on the Board of Directors of a company. The probabilities of their winning are 0.5,0.3,0.2 respectively. If the group ( A ) wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for groups ( B ) and ( C ) are 0.6 and 0.5 respectively. The probability that the new product will be introduced is given by A . 0.36 в. 0.35 c. 0.63 D. 0.53 | 12 |

1561 | t is known that an urn containing altogether 10 balls was filled in the following manner: A coin was tossed 10 times, and according as it showed heads or tails, one white or on black ball was put into the urn. Balls are drawn from this urn one at a time, 10 times in succession (with replacements) and every one turns out to be white. The chance that the urn contains nothing but white balls is ( frac{1}{2^{k}} . ) Find the value of ( k ) | 12 |

1562 | A biased com wih probatnity ( mathrm{p}, 0<mathrm{p}<1 ) of heads is tossed until a head appears for the first time. If the probatory that the number of tosses required is even is ( 2 / 5 ) find the value of ( p ) | 12 |

1563 | If the probability of India winning a particular hockey match is ( 0.81 . ) What is the probability of India losing that match? A . 0.19 B. 0.29 c. 0.59 D. 0.49 | 12 |

1564 | Three unbiased coins are tossed together. Find the probability of getting 1. Two heads. 2. At least two heads. 3. No heads | 12 |

1565 | If ( P(A)=0.4, P(B)=0.3 ) and ( P(B / A)=0.5, ) find ( P(A cap B) ) and ( P(A / B) ) | 12 |

1566 | An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let ( boldsymbol{X} ) represent the number of black balls. What are the possible values of ( X ? ) Is ( X ) a random variable ? ( mathbf{A} cdot 0,1,2 ) в. 3,5,7 c. 7,7,8 D. 1,5,7 | 12 |

1567 | Ar a selection, the probability of selection of ( A ) is ( frac{1}{7} ) and that of 8 is ( frac{1}{5} . ) If ( A ) and ( B ) are independent events, then the probability that neither of them would be selected is ? | 12 |

1568 | Which of the following is an example of a random experiment? This question has multiple correct options A. Selecting a card from a pack of playing cards. B. Measuring the weight of a person. C. Finding the length of your pencil box. D. Throwing two coins together. | 12 |

1569 | A box contains 1 red and 3 identica white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment. | 12 |

1570 | One of the two events must happen. Given that the chance of one is two- third of the other, find the odds in favour of the other. | 12 |

1571 | In a non-leap year the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is. A ( cdot frac{1}{7} ) B. ( frac{2}{7} ) ( c cdot frac{3}{7} ) D. ( frac{4}{7} ) | 12 |

1572 | A bag contains 15 red, 8 blue and several green marbles. A marble is selected at random. The probability of drawing a blue marble is ( frac{1}{5} ) 5 green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing a green marble A ( cdot frac{3}{10} ) В. ( frac{12}{35} ) c. ( frac{23}{40} ) D. ( frac{17}{35} ) | 12 |

1573 | The sum of 5 digit numbers such that the sum of their digit is even is : ( mathbf{A} .50000 ) B. 45000 c. 60000 ( D cdot ) none | 12 |

1574 | Identify the experiment for the statement “Toss a coin to get head or tail”. A. Tossing a coin B. Rolling of a dice c. Throw a die D. Pick a card | 12 |

1575 | A bag contains 4 white, 5 red and 6 black balls. Three are drawn at random. Find the probability that (i) no ball drawn is black, (ii) exactly 2 are black (iii) all are of the same colour. A ( cdot frac{12}{65}, frac{27}{91}, frac{6}{91} ) В. ( frac{12}{65}, frac{27}{91}, frac{24}{455} ) c. ( frac{12}{65}, frac{27}{91}, frac{14}{455} ) D. ( frac{12}{65}, frac{27}{91}, frac{34}{455} ) | 12 |

1576 | If ( A ) and ( B ) are two mutually exclusive events such that ( P(A)=0.55 ) and ( P(B)=0.35 ) then ( P(bar{A} cup bar{B})= ) A ( cdot frac{1}{4} ) B. ( c ) D. | 12 |

1577 | Given a circle of radius ( R ), the experiment is to randomly select a chord in that circle. Identify the type of the sample space. A. Finite sample space B. Continuous sample space c. Infinite discrete sample space D. None of these | 12 |

1578 | An urn contains 5 red and 5 black balls A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red? | 12 |

1579 | When a die is thrown, list the outcomes of an event of getting: a number lesser than 5 A .1,2,3,4 B. 1,2,3 c. 3,4,5 D. 4,5 | 12 |

1580 | If ( r cdot v cdot X sim Bleft(n=5, P=frac{1}{3}right), ) then ( P(2<X<4)=ldots . ) A. ( frac{80}{243} ) B. ( frac{40}{243} ) c. ( frac{40}{343} ) D. ( frac{80}{343} ) | 12 |

1581 | For the three events ( A, B & C ) probability of exactly one of the events ( A ) or ( B ) occurs ( = ) probability of exactly one of the events ( C ) or ( A ) occurs ( =p & P ) (all the three events occur simultaneously) ( =p^{2}, ) where A ( cdot frac{3 p+2 p^{2}}{2} ) в. ( frac{p+3 p^{2}}{4} ) c. ( frac{p+3 p^{2}}{2} ) D. ( frac{3 p+2 p^{2}}{4} ) | 12 |

1582 | Two bad eggs are accidentally mixed up with ten good ones. Find the probability of picking good eggs. | 12 |

1583 | Given that the events ( A ) and ( B ) are such ( operatorname{that} boldsymbol{P}(boldsymbol{A})=frac{1}{2}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{boldsymbol{3}}{mathbf{5}} ) and ( boldsymbol{P}(boldsymbol{B})=boldsymbol{p} . ) Find ( boldsymbol{p} ) if they are (i) mutually exclusive (ii) independent. A . 0.5,0.6 в. 0.1,0.2 c. 0,2,0.4 D. 0.1,0.6 | 12 |

1584 | A boy contains 100 bolts and 50 nuts. It is given that ( 50 % ) bolts and ( 50 % ) nuts are rusted. Two objects are selected from the box at random. Find the probability that both are bolts or both are rusted. | 12 |

1585 | A pair of dice is thrown 4 times. If getting a total of 9 in a single throw is considered as a success then find the mean and variance of successes. | 12 |

1586 | One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)? A ( cdot frac{1}{13} ) в. ( frac{2}{13} ) c. ( frac{3}{13} ) D. ( frac{4}{13} ) | 12 |

1587 | A purse contains four coins each of which is either a rupee or two rupees coin. Find the expected value of a coin in that purse. | 12 |

1588 | Out of 35 students participating in a debate 10 are girls The probability that the winner is a boy will be A ( cdot frac{3}{7} ) B. c. ( frac{1}{7} ) D. ( frac{2}{7} ) | 12 |

1589 | If ( mathbf{a} in[-mathbf{1 0}, mathbf{0}] ) then the probability that the graph of the function ( mathbf{y}=mathbf{x}^{2}+ ) ( 2(a+3) x-(2 a+3) ) is strictly above ( x ) axis is A ( cdot frac{3}{5} ) B. ( frac{2}{5} ) ( c cdot frac{1}{5} ) D. ( frac{4}{5} ) | 12 |

1590 | A pair of dice is thrown 4 times, then the probability of getting doublets at least twice is A ( cdot frac{19}{44} ) в. ( frac{21}{44} ) ( c cdot frac{31}{44} ) D. ( frac{39}{44} ) | 12 |

1591 | Exactly 6 on each of 3 successive throws A ( cdot frac{5^{3}}{16^{3}} ) в. ( frac{5}{16^{3}} ) c. ( frac{5^{2}}{16^{3}} ) D. ( frac{1}{16^{3}} ) | 12 |

1592 | In a single throw of a die, the probability of getting a multiple of 3 is A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{1}{6} ) D. ( frac{3}{4} ) | 12 |

1593 | For any two events ( A ) and ( B ) ( mathbf{A} cdot P(A)+P(B)>P(A cap B) ) B ( cdot P(A)+P(B)<P(A cap B) ) ( mathbf{c} cdot P(A)+P(B) geq P(A cap B) ) D ( . P(A)+P(B) leq P(A cap B) ) | 12 |

1594 | Two cards are drawn simultaneously (without replacement) from a well- shuffled pack of 52 cards. Find the mean and variance of the number of red cards. ( mathbf{A} cdot ) Mean ( =0.1 ) and Variance ( =0.7 ) B. Mean ( =0.6 ) and Variance ( =0.3 ) C . Mean ( =0.49 ) and Variance ( =0.37 ) D. Mean ( =0 ) and Variance ( =0.45 ) | 12 |

1595 | If the probability of selecting a bolt from 400 bolts is ( 0.1, ) then the mean for the distribution is A . 0.09 B . 40 ( c .36 ) D. 360 | 12 |

1596 | When a die is thrown, list the outcomes of an event of getting prime number. A ( cdot{2,3,5} ) в. {2,4,6} D. {1,3,5} | 12 |

1597 | A dice is thrown once,what is the probability of getting an even prime number. A ( cdot frac{1}{2} ) B. ( frac{2}{3} ) ( c cdot frac{1}{4} ) D. | 12 |

1598 | is an action where the result is uncertain. A. Space B. Sample c. Experiment D. Event | 12 |

1599 | A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white. | 12 |

1600 | The odds against A solving a problem are 8 to 6 and the odds in favour of ( B ) solving the same problem 14 to ( 12 . ) The probability of solving the problem if they both try independently is A ( cdot frac{67}{91} ) в. ( frac{5}{21} ) c. ( frac{4}{21} ) D. | 12 |

1601 | u) 0/3 (b) 3/8 (c) 4/5 tu) The mean and variance of a random varie al distribution are 4 and 2 respectively, then e of a random variable X having is 120031 th | 12 |

1602 | Which of the following is true regarding law of total probability? A. It is a fundamental rule relating marginal probabilities to conditional probabilitities. B. It expresses the total probability of an outcome which can be realized via several distinct events c. Both are correct D. None of these | 12 |

1603 | The sum of the probabilities of each outcome in an experiment is | 12 |

1604 | Three coins are tossed. Describe two events ( A ) and ( B ) which are not mutually exclusive. | 12 |

1605 | What is the probability that the wheel stops at red or pink? ( mathbf{A} ) ( B ) 6 ( c cdot 3 ) D. None of these | 12 |

1606 | The probability of an event can be greater than: ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) ( D ) | 12 |

1607 | The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is: A . B. 2 c. 5 D. ( frac{8}{3} ) | 12 |

1608 | ( ln ) a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is ( 1 / 3 & ) the probability that he copies the answer is ( 1 / 6 . ) The probability that his answer is correct given that he copied it, is ( 1 / 8 . ) Find the probability that he knew the answer to the question given that he correctly answered it. If expressed in the form of ( a / b ) (simplest form), ( b-a=? ) | 12 |

1609 | A car is parked among ( N ) cars standing in a row, but not at either end. On his return, the owner finds that exactly ( r ) of the ( N ) places are still occupied. What is the probability that both the places neighboring his car are empty? A ( . ) Required probability ( =frac{(N-r)(N-r-2)}{(N-1)(N-2)} ) B. Required probability ( =frac{(N-r)(N-r-1)}{(N-1)(N-2)} ) c. Required probability ( =frac{(N-r-2)(N-r-1)}{(N-1)(N-2)} ) D. none of these | 12 |

1610 | If ( P(A)=frac{1}{4}, P(bar{B})=frac{1}{2} ) and ( P(A cup ) B) ( =frac{5}{9}, ) then ( P(A / B) ) is ( ^{A} cdot frac{7}{36} ) в. c. ( frac{7}{18} ) D. ( frac{7}{72} ) | 12 |

1611 | A die is thrown. Find the probability of getting a prime number. | 12 |

1612 | Two coins are tossed 1000 times and the outcomes are recorded as below: ( mathbf{2} ) No of heads ( mathbf{0} ) 250 Frequency ( 200 quad 550 ) Based on this information, the probability for at most one head is ( frac{a}{b} ) Where ( (a, b)=1, ) then A ( cdot frac{1}{5} ) в. ( c cdot frac{4}{5} ) D. | 12 |

1613 | Find the number of numbers of 5 digits that can be formed with the digits 0,1,2,3,4 if the digits can be repeated in the same number. | 12 |

1614 | Let A, B, C be three mutually independent events. Consider the two statements S, and S2 S: A and B u C are independent S: A and B C are independent Then, (1994) (a) Both S, and S, are true (b) Only S, is true (C) Only S, is true (d) Neither S, nor S, is true | 12 |

1615 | If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) then find ( boldsymbol{P}(overline{boldsymbol{A}} cap overline{boldsymbol{B}}) ) | 12 |

1616 | 15. The probabilities that a student passes in Mathematics, Physics and Chemistry are m,p and c, respectively. Of these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two, and a 40% chance of passing in exactly two. Which of the following relations are true? (1999 – 3 Marks) (a) p+m+c= 19/20 (b) p+m+c=27/20 (c) pmc=1/10 (d) pmc=1/4 | 11 |

1617 | A die is thrown. Find the probability of getting an odd number | 12 |

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