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JEE Main Probability questions

56 Mathematics questions on Probability as asked in JEE Main, newest first. 41 come with a worked solution.

  1. Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ^2 represent mean and…

    2023 · with solution

  2. Let Ω be the sample space and A ⊂eq Ω be an event. Given below are two statements : (S1) : If P(A) = 0, then A = emptyset (S2) : If P(A) = 1, then A = Ω Then

    2023 · with solution

  3. Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x + y + z = 1 2x + Ny + 2z = 2 3x + 3y + Nz = 3 has unique solution is k/6, then the sum of value of k and…

    2023 · with solution

  4. Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, √(3N), N+2 are in geometric progression be k/48. Then the value of k is

    2023 · with solution

  5. Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is…

    2023 · with solution

  6. 25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that that person is a smoker is k/10. Then the…

    2023

  7. A person throws two fair dice. He wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and loses ₹ 6 for any other outcome on the throw. Then, the expected…

    2019 · with solution

  8. For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 4/5, then the probability that he is unable to solve less than…

    2019

  9. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls; is

    2019 · with solution

  10. A pot contain 5 red and 2 green balls. At random a ball is drawn from this pot. If a drawn ball is green then put a red ball in the pot and if a drawn ball is red, then put a green ball in the pot, while drawn ball is…

    2019

  11. 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

    2019

  12. Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X ≤ 2) = dfrack2^16, then k is equal to

    2019 · with solution

  13. Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is

    2019 · with solution

  14. Minimum number of times a fair coin must be tossed so that the probability of getting atleast one head is more than 99% is

    2019 · with solution

  15. If there of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is

    2019 · with solution

  16. Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct.

    2019 · with solution

  17. Two integers are selected at random from the set \1, 2, ……, 11\. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

    2019 · with solution

  18. The minimum number of times one has to toss a fair coin so that the probability of observing atleast one head is atleast 90% is

    2019 · with solution

  19. An unbiased coin is tossed. If the outcome is a head, then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail, then a card from a…

    2019

  20. In a game, a man wins ₹100 if he gets 5 or 6 on a throw of a fair die and loses ₹50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three…

    2019

  21. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then, P(X=1) + P(X=2) equals

    2019 · with solution

  22. A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at…

    2018 · with solution

  23. For three events A, B and C, if P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = 1/4 and P(all the three events occur simultaneously) = 1/16, then the probability…

    2017 · with solution

  24. If two different numbers are taken from the set {0, 1, 2, 3, ..., 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is

    2017 · with solution

  25. 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

    2017 · with solution

  26. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is

    2017 · with solution

  27. 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 the total computers produced. 7% of computers produced in the factory turn out to be defective. It is…

    2016

  28. If 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains exactly 3 balls, is

    2015

  29. Let A and B be two events such that P(A ∪ B) = 1/6, P(A ∩ B) = 1/4 and P(A) = 1/4, where A stands for the complement of the event A. Then, the events A and B are

    2014 · with solution

  30. Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is atleast one more that the number of girls ahead of her, is

    2014 · with solution

  31. Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then, the probability that the problem is solved correctly by atleast one of them, is

    2013 · with solution

  32. 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

    2013 · with solution

  33. Four fair dice D_1, D_2, D_3 and D_4 each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that D_4 shows a number appearing on one of D_1, D_2 and D_3, is

    2012

  34. Let ω be a complex cube root of unity with ω ≠ 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 ω^r_1 + ω^r_2 + ω^r_3 = 0, is

    2010

  35. An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of outcomes that B must have, so that A and B are independent, is

    2008 · with solution

  36. Let E^c denotes the complement of an event E. If E, F, G are pairwise independent events with P(G) > 0 and P(E ∩ F ∩ G) = 0. Then, P(E^c ∩ F^c | G) equals

    2007 · with solution

  37. A fair die is rolled. The probability that the first time 1 occurs at the even throw, is

    2005

  38. 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

    2004 · with solution

  39. Two numbers are selected randomly from the set S = \1, 2, 3, 4, 5, 6\ without replacement one by one. The probability that minimum of the two numbers is less than 4, is

    2003 · with solution

  40. If P(B) = 3/4, P(A ∩ B ∩ C) = 1/3 and P(A ∩ B ∩ C) = 1/3, then P(B ∩ C) is equal to

    2002 · with solution

  41. If E and F are events with P(E) ≤ P(F) and P(E ∩ F) > 0, then which one is not correct?

    1998

  42. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

    1998 · with solution

  43. Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

    1998 · with solution

  44. 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 balls will be drawn, is

    1998 · with solution

  45. For the three events A, B and C, P(exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P(all the three events occurs simultaneously)…

    1996

  46. If 0 < P(A) < 1, 0 < P(B) < 1 and P(A ∪ B) = P(A) + P(B) - P(A)P(B), then

    1995 · with solution

  47. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

    1995 · with solution

  48. 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

    1995 · with solution

  49. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50, respectively. Assuming that the outcomes are independent. The…

    1992

  50. 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…

    1988

  51. 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 equal to

    1987 · with solution

  52. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2,…

    1986 · with solution

  53. Three identical dice are rolled. The probability that the same number will appear on each of them, is

    1984 · with solution

  54. If A and B are two independent events such that P(A) > 0, and P(B) ≠ 1, then P(A/B) is equal to

    1982 · with solution

  55. 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 · with solution

  56. The probability that an event A happens in one trial of an experiment, is 0.4. Three independent trials of the experiments are performed. The probability that the event A happens atleast once, is

    1980 · with solution

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