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# JEE Main 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 Main Math Previous Year Paper Probability Questions Answer Keys Solutions.

### JEE Mains Mathematics Probability Questions Bank

JEE Probability Questions No:1

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of is



Option A: 8 / 3

Option B: 3 / 8

Option C: 4 / 5

Option D: 5 / 4

Option D: 5 / 4

JEE Main Probability Questions No:2

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is (1 / 2), (1 / 3), and (1 / 4). Probability that the problem is solved is



Option A: 3 / 4

Option B: 1 / 2

Option C: 2 / 3

Option D: 1 / 3

Option A: 3 / 4

JEE Mathematics Probability Questions No:3

A and B are events such that P (AUB) = (3/4). P (A ∩ B) = (1/4), P(A)= (2/3) then P(A ∩ B) is



Option A: 5/12

Option B: 3/8

Option C: 5/8

Option D: 1/4

Option A: 5/12

JEE Main Math Probability Questions No:4

The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is



Option A: 1 / 4

Option B: 1 / 32

Option C: 1 / 16

Option D: 1 / 8

Option B: 1 / 32

Probability JEE Questions No:5

Events A, B, C are mutually exclusive events such that P (A) = (3X + 1 / 3), P (B) = (1 – x / 4 ) and P (C) = (1 – 2x / 2).The set of possible values of x are in the interval



Option A: [ (1/3), (1/2) ]

Option B: [ (1/3), (2/3) ]

Option C: [ (1/3), (13/3) ]

Option D: [ 0, 1 ]

Option C:  [ (1/3), (13/3) ]

Probability JEE Main Questions No:6

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is



Option A: 4/5

Option B: 3/5

Option C: 1/5

Option D: 2/5

Option D: 2/5

Probability Questions for JEE Mains Questions No: 7

A random variable X has the probability distribution: For the events E = { X is a prime number } and F = {X < 4}, the P(E ∪ F) is



Option A: 0.50

Option B: 0.77

Option C: 0.35

Option D: 0.87

Option B: 0.77

Probability Questions and Answers No:8

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is



Option A: 28 / 256

Option B: 219 / 256

Option C: 128 / 256

Option D: 37 / 256

Option A:  28 / 256

Probability Questions with Solutions No:9

The probability that A speaks truth is (4/5) while the probability for B is (3/4). The probability that they contradict each other when asked to speak on a fact is



Option A: 4/5

Option B: 1/5

Option C: 7/20

Option D: 3/20

Option C:  7/20

JEE Mains Probability Questions No: 10

A random variable X has Poisson distribution with mean 2 Then P (X > 1.5) equals



Option A: 2 / e2

Option B: 0

Option C: 1 – (3 / e2)

Option D: 3 / e2

Option C: 1 – (3 / e2)

JEE Mains Math Probability Questions No: 11

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 complement of event A. Then events A and B are



Option A: Equally likely and mutually exclusive

Option B: Equally likely but not independent

Option C: Independent but not equally likely

Option D: Mutually exclusive and independent

Option C:  Independent but not equally likely

Probability Questions for JEE Questions No: 12

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



Option A: 2/9

Option B: 1/9

Option C: 8/9

Option D: 7/9

Option B: 1/9

Probability Problems for Class 11 Questions No:13

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is



Option A: 6 / 5e

Option B: 5 / 6

Option C: 6 / 55

Option D: 6 / e5

Option D: A6 / e5

Probability Problems for Class 12 Questions No: 14

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is



Option A: 8 / 729

Option B: 8 / 243

Option C: 1 / 729

Option D: 8 / 9

Option B: 8 / 243

Probability Problems for Class 11 JEE Questions No: 15

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II 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



Option A: 0.2

Option B: 0.7

Option C: 0.06

Option D: 0.14

Option D:  0.14

Probability Problems for Class 12 JEE Questions No:16

It is given that the events A and B are such that P (A) = (1/4), P(A/B) = (1/2) and P(B/A) = (2/3). Then P(B) is



Option A: 1/6

Option B: 1/3

Option C: 2/3

Option D: 1/2

Option B:  1/3

JEE Probability Questions No:17

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A U B) is



Option A: 3/5

Option B: 0

Option C: 1

Option D: 2/5

Option C: 1

JEE Main Probability Questions No:18

In a binomial distribution B (n, p = (1/4) ), if the probability of at least one success is greater than  equal (9/ 10) to then n is greater than:



Option A: 1 / log10 4 + log10 3

Option B: 9 / log10 4 – log10 3

Option C: 4 / log10 4 – log10 3

Option D: 1 / log10 4 – log10 3

Option D: 1 / log10 4 – log10

JEE Mathematics Probability Questions No: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 8, given that the product of these digits is zero, equals:



Option A: 1/7

Option B: 5/14

Option C: 1/50

Option D: 1/14

Option D:  1/14

JEE Main Math Probability Questions No:20

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is



Option A: 36

Option B: 66

Option C: 108

Option D: 3

Option C: 108

Probability JEE Questions No:21

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the um. The probability that the three balls have different colour is



Option A: 2/7

Option B: 1/21

Option C: 2/23

Option D: 1/3

Option A: 2/7

Probability JEE Main Questions No:22

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to (31/32) then p lies in the interval



Option A: (3/4, 11/12]

Option B: [0, 1/2]

Option C: (11/12, 1]

Option D: (1/2, 3/4]

Option B: [0, 1/2]

Probability Questions for JEE Mains Questions No: 23

Let A, B, C be pairwise independent events with P(C) > 0 and P(A ∩ B ∩ C) = 0. Then P(AC ∩ BC | C) is equal to



Option A: P(AC ) – P(BC)

Option B: P(AC ) – P(B)

Option C: P(A) – P(BC)

Option D: P(AC ) + P(BC)

Option B: P (AC) – P(B)

Probability Questions and Answers No: 24

Three numbers are chosen at random without replacement from (1,2,3,..8). The probability that their minimum is 3, given that their maximum is 6 is



Option A: 3/8

Option B: 1/5

Option C: 1/4

Option D: 2/5

Option B: 1/5

Probability Questions with Solutions No: 25

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:



Option A: 17 / 35

Option B:  13 / 35

Option C: 11 / 35

Option D: 10 / 35

Option C: 11 / 35

JEE Mains Probability Questions No: 26

Given two independent events, if the probability that exactly one of them occurs is (26/49) and the probability that none of them occurs is (15/49) then the probability of more probable of the two events is:



Option A: 4/7

Option B: 6/7

Option C: 3/7

Option D: 5/7

Option A: 4/7

JEE Mains Math Probability Questions No: 27

If X has a binomial distribution, B(n, p) with parameters n and p such that P (X = 2) = P (X = 3), then E (X), the mean of variable X, is



Option A: 2 – p

Option B:  3 – p

Option C: p / 2

Option D: p / 3

Option B: 3 – p

Probability Questions for JEE Questions No: 28

Let A and E be any two events with positive probabilities

Statement-1: P(E / A) ≥ P(A / E) P(E)

Statement-2: P(A / E) ≥ P(A E)



Option A: Both the statements are true

Option B: Both the statements are false

Option C: Statement-1 is true, Statement-2 is false

Option D: Statement-1 is false, Statement-2 is true

Option A: Both the statements are true

Probability Problems for Class 11 Questions No:29

Let A and B be two events such that P(A U 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



Option A: Independent but not equally likely.

Option B: Independent and equally likely.

Option C: Mutually exclusive and independent.

Option D: Equally likely but not independent

Option A: Independent but not equally likely

Probability Problems for Class 12 Questions No: 30

If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is :



Option A: 9 / 16

Option B: 3 / 4

Option C: 1 / 16

Option D: 15 / 16