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# JEE Math Previous Year Papers Probability Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Math Previous Year Papers Probability Questions Answer Keys Solutions.

### JEE Mains Mathematics Probability Questions Bank

Probability Problems for Class 11 JEE Questions No: 31

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is



Option A: 1/21

Option B: 1/27

Option C: 1/15

Option D: 1/26

Option B: 1/27

Probability Problems for Class 12 JEE Questions No:32

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number elements, is



Option A: (210 – 1) / 210

Option B: 20C10 / 210

Option C: (210 – 1) / 220

Option D: 20C10 / 220

Option D: 20C10 / 220

JEE Probability Questions No: 33

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



Option A: 55 (2/3)10

Option B: 220 (1/3)12

Option C: 22 (1/3)11

Option D: (55/3) (2/3)11

Option : None of These

JEE Main Probability Questions No: 34

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is:



Option A: 496 / 729

Option B: 192 / 729

Option C: 240 / 729

Option D: 256 / 729

Option D:  256 / 729

JEE Mathematics Probability Questions No:35

If A and B are any two events such that P(A) = 2/5, P(A ∩ B) = 3/20 then the conditional probability, P(A | A’ U B’) ), where A’ denotes the complement of A, is equal to



Option A: 11 / 20

Option B: 5 / 17

Option C: 8 / 17

Option D: 1 / 4

Option B: 5 / 17

JEE Main Math Probability Questions No:36

Let two fair six-faced dice A and B be thrown simultaneously. If E1, is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?



Option A: E1 and E3are independent

Option B: E1,E2 are E3 are independent

Option C: E1 and E2 are independent

Option D: E2 and E3 are independent

Option B: E1, E2 and E3 are independent

Probability JEE Questions No:37

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :



Option A: 255 / 256

Option B: 127 / 128

Option C: 63 / 64

Option D: 1 / 2

Option B: 127 / 128

Probability JEE Main Questions No: 38

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



Option A: 6 / 25

Option B: 12 / 5

Option C: 6

Option D: 4

Option B: 12 / 5

Probability Questions for JEE Mains Questions No: 39

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are (3/4), (1/2) and (5/8)  respectively, then the probability that the target is hit by P or Q but not by R is be



Option A: 21/64

Option B:  9/64

Option C: 15/64

Option D: 39/64

Option A: 21/64

Probability Questions and Answers No: 40

Let E and F be two independent events. The probability that both E and F happen is (1/12) and the probability that neither E nor F happens is (1/2), then a value pf P(E) / P(F) is



Option A: 4/3

Option B: 3/2

Option C: 1/3

Option D: 5/12

Option A: 4/3

Probability Questions with Solutions No: 41

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



Option A: 7/55

Option B:  6/55

Option C: 12/55

Option D: 14/55

Option B: 6/55

JEE Mains Probability Questions No: 42

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) = (1/4) and P(All the three events occur simultaneously) = (1/16). Then the probability that at least one of the events occurs, is



Option A: 7/32

Option B: 7/16

Option C: 7/64

Option D: 3/16

Option B: 7/16

JEE Mains Math Probability Questions No: 43

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ‘p’ is



Option A: 1 / 3

Option B: 1 / 5

Option C: 1 / 4

Option D: 2 / 5

Option A: 1 / 3

Probability Questions for JEE Questions No: 44

A box ‘A’ contains 2 white, 3 red and 2 black balls. Another box ‘B’ 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’ is



Option A: 7/16

Option B: 9/32

Option C: 7/8

Option D: 9/16

Option A:  7/16

Probability Problems for Class 11 Questions No:45

Let A, B and C be three events, which are pair-wise independence and E denotes the complement of an event E. If P (A ∩ B ∩ C) = 0 and P (C) > 0, then P[ (A ∩ B) | C ] is equal to



Option A:  P (A) + P (B)

Option B:  P(A) – P(B)

Option C:  P(A) – P (B)

Option D:  P(A) + P(B)

Option C:  P(A) – P(B)

Probability Problems for Class 12 Questions No: 46

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 random from the bag, then the probability that this drawn ball is red is



Option A: 2/5

Option B: 1/5

Option C:  3/4

Option D: 3/10

Option A:  2/5

Probability Problems for Class 11 JEE Questions No: 47

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



Option A: 49 / 169

Option B: 52 / 169

Option C: 24 / 169

Option D: 25 / 169

Option D: 25 / 169

Probability Problems for Class 12 JEE Questions No: 48

If the probability of hitting a target by a shooter, in any shot, is (1/3) then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than (5/6) is:



Option A: 3

Option B: 6

Option C: 5

Option D: 4

Option C: 5

JEE Probability Questions No: 49

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then ( mean of X / standard deviation of X) is equal to



Option A: 4

Option B:  4√3

Option C: 3√2

Option D: 4√3/ 3

Option B: 4√3

JEE Main Probability Questions No: 50

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 throws, then his expected gain/loss (in rupees) is



Option A: (400 / 9) loss

Option B: 0

Option C: (400 / 3) gain

Option D: (400 / 3) loss

Option B: 0

JEE Mathematics Probability Questions No:51

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is:



Option A: 5

Option B: 6

Option C: 8

Option D: 7

Option D: 7

JEE Main Math Probability Questions No:52

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 two problems is :



Option A: (201 / 5) (1 / 5)49

Option B: (316 / 25) (4 / 5)48

Option C: (54 / 5) (4 / 5)49

Option D: (164 / 25) (1 / 5)48

Option C:  (54 / 5) (4 / 5)49

Probability JEE Questions No: 53

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



Option A: 1 / 2 gain

Option B: 1 / 4 loss

Option C: 1 / 2 loss

Option D: 2 gain

Option C: 1 / 2 loss

Probability JEE Main Questions No: 54

Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X ≤ 2) = (k / 216), then k is equal to:



Option A: 17

Option B: 121

Option C: 1

Option D: 137

Option D: 137

Probability Questions for JEE Mains Questions No: 55

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is



Option A: 21/49

Option B:  27/49

Option C:  26/49

Option D: 32/49

Option D: 32/49

Probability Questions and Answers No: 56

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 well-shuffled pack of nine cards numbered 1, 2, 3,…, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is



Option A: 13/36

Option B:  15/72

Option C: 19/72

Option D: 19/36

Option C: 19/72

Probability Questions with Solutions No: 57

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:



Option A: 7/10

Option B: 1/2

Option C: 2/5

Option D: 3/5

Option C: 2/5

JEE Mains Probability Questions No: 58

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



Option A: 200/65

Option B: 150/65

Option C: 225/65

Option D: 175/65

Option D: 175/65

JEE Mains Math Probability Questions No: 59

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



Option A: P(A | B) = P(B) – P(A)

Option B: P(A | B) ≥ P(A)

Option C: P(A | B) ≤ P(A)

Option D: P(A | B) = 1

Option B: (A | B) ≥ P(A)

Probability Questions for JEE Questions No: 60

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



Option A: 25/192

Option B: 7/32

Option C: 1/192

Option D: 25/32