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# JEE Main Math 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 Probability Questions Answer Keys Solutions.

### JEE Mains Mathematics Probability Questions Bank

Probability Problems for Class 11 Questions No: 61

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]

Option A: 1/11

Option B: 1/10

Option C: 1/12

Option D: 1/17

Option A: 1/11

Probability Problems for Class 12 Questions No: 62

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is (1/4). If the probability that at most two machines will be out of service on the same day is (3/4)3k, then k is equal to:

[2020]

Option A: 17 / 8

Option B: 17 / 4

Option C: 17 / 2

Option D: 4

Option A: 17 / 8

Probability Problems for Class 11 JEE Questions No: 63

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is:

[2020]

Option A: 3 / 16

Option B: 1 / 8

Option C: -3 / 16

Option D: -1 / 8

Option B: 1 / 8

Probability Problems for Class 12 JEE Questions No: 64

A random variable X has the following probability distribution:

Then, P(X > 2) is equal to:

[2020]

Option A: 7 / 12

Option B: 1 / 36

Option C: 1 / 6

Option D: 23 / 36

Option D: 23 / 36

JEE Probability Questions No: 65

The probability of a man hitting a target is (1/10). The least number of shots required, so that the probability of his hitting the target at least once is greater than (1/4) is

[2020]

Correct Ans : 3

JEE Main Probability Questions No: 66

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is

[2020]

Correct Ans : 11

JEE Mathematics Probability Questions No: 67

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is

[2020]

Correct Ans : 11

JEE Main Math Probability Questions No:68

Let A and B be two independent events such that P(A) = (1/3) and P(B) = (1/6) Then, which of the following is TRUE?

[2020]

Option A: P(A / B) = (2/3)

Option B: P(A / B’) = (1/3)

Option C: P(A’ / B’) = (1/3)

Option D: P(A / (A ∪ B )) = (1/4)

Option B: P(A / B’) = (1/3)

Probability JEE Questions No: 69

In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is

[2020]

Option A: 9/16

Option B: 11/16

Option C: 13/16

Option D: 15/16

Option B: 11/16

Probability JEE Main Questions No: 70

Let EC denote the complement of an event E. Let E1, E2, and E3, be any pairwise independent events with P(E1) > 0 and P(E1 ∩ E2 ∩ E3) = 0 Then P(EC2 ∩ EC3 / E1) is equal to

[2020]

Option A: P(EC2 ) + P(E3)

Option B: P(EC3 ) – P(EC2 )

Option C: P(E3)) – P(EC2)

Option D: P(EC3 ) – P(E2)

Option D: P(EC3) – P(E2)

Probability Questions for JEE Mains Questions No: 71

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box l is

[2020]

Option A: 2/3

Option B: 8/17

Option C: 4/17

Option D: 2/5

Option B: 8/17

Probability Questions and Answers No: 72

The probability that a randomly chosen 5-digit number is made from exactly two digits is made from exactly two digits is

[2020]

Option A: 135/104

Option B: 121/104

Option C: 150/104

Option D: 134/104

Option A: 135/104

Probability Questions with Solutions No: 73

A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is

[2020]

Option A: 1/4

Option B: 1/3

Option C: 1/8

Option D: 1/9

Option D: 1/9

JEE Mains Probability Questions No: 74

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before 4 throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is

[2020]

Option A: 5/31

Option B: 31/61

Option C: 5/6

Option D: 30/61

Option D:  30/61

JEE Mains Math Probability Questions No: 75

Let in a binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to

[2021]

Option A: 80 / 243

Option B: 32 / 625

Option C: 40 / 243

Option D: 128 / 625

Option B:  32 / 625

Probability Questions for JEE Questions No: 76

A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X ≥ 5 | X > 2) is:

[2021]

Option A: 125 / 216

Option B: 11 / 36

Option C: 5 / 6

Option D: 25 / 36

Option D: 25 / 36

Probability Problems for Class 11 Questions No: 77

The probability distribution of random variable X is given by:

Let p = P(1 < X < 4 | X < 3). If 5p = λK, then λ equal to

[2021]

Correct Ans : 30

Probability Problems for Class 12 Questions No: 78

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5) have exactly two elements in their intersection, is

[2021]

Option A: 65/27

Option B: 65/28

Option C: 135/29

Option D: 35/27

Option C: 135/29

Probability Problems for Class 11 JEE Questions No: 79

Let Bi,(i = 1, 2, 3) be three independent events in a sample space. The probability that only β, occur is α. Only B2, occurs is β and only B3, occurs is ɣ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α-2β) p = αβ and (β – 3ɣ) p = 2βɣ (All the probabilities are assumed to lie in the interval (0, 1)). Then ( P(B1) / P(B3) ) is equal to

[2021]

Correct Ans: 6

Probability Problems for Class 12 JEE Questions No: 80

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is

[2021]

Option A: 2/9

Option B: 97/297

Option C: 122/297

Option D: 1/5

Option B:  97/297

JEE Probability Questions No: 81

When a missile is fired a ship, the probability that it is intercepted is (1/3) and the probability that the missile hits the target, given that it is not intercepted, is (3/4). If three missiles are fired independently from the ship, then the probability that all three hit the target, is

[2021]

Option A: 1/27

Option B: 3/8

Option C: 3/4

Option D: 1/8

Option D: 1/8

JEE Main Probability Questions No: 82

A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is

[2021]

Option A: 1/7

Option B:  6/7

Option C: 4/7

Option D: 3/7

Option D: 3/7

JEE Mathematics Probability Questions No: 83

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is

[2021]

Option A: 15/213

Option B: 15/212

Option C: 15/28

Option D: 15/214

Option A: 15/213

JEE Main Math Probability Questions No: 84

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is

[2021]

Option A: 52/867

Option B: 22/425

Option C: 3/4

Option D: 39/50

Option D: 39 / 50

Probability JEE Questions No: 85

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be (1/2) and probability of occurrence of 0 at the odd place be (1/3). Then the probability that ’10’ is followed by ’01’ is equal to

[2021]

Option A: 1/18

Option B: 1/3

Option C: 1/6

Option D: 1/9

Option D: 1/9

Probability JEE Main Questions No: 86

Let there be three independent events E1, E2 and E3. The probability that only E1, occurs is ⍺, only E2, occurs is β and only E3, occurs is ɣ. Let ‘p’ denote the probability of none of events occurs that satisfies the equations (⍺ – 2β)p = ⍺β and (β – 3ɣ)p = 2βɣ. All the given probabilities are assumed to lie in the interval (0, 1).Then, (Probability of occurrence of E1 / Probability of occurrence of E3) is equal to

[2021]

Correct Ans : 6

Probability Questions for JEE Mains Questions No: 87

Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 – k), the probability that exactly one of B and C occurs is (1 – 2k), the probability that exactly one of C and A occurs is (1 – k) and the, probability of all A, B and C occur simultaneously is k2,where 0 < k < 1. Then the probability that at least one of A, B and C occur is

[2021]

Option A: Greater than (1/8) but less than (1/4)

Option B: Greater than (1/2)

Option C: Greater than (1/4) but less than (1/2)

Option D: Exactly equal to (1/2)

Option B: Greater than (1/2)

Probability Questions and Answers No: 88

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is

[2021]

Option A: 1/66

Option B: 1/11

Option C: 1/9

Option D: 2/11

Option B:  1/11

Probability Questions with Solutions No: 89

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrices have all different 7 entries and are non-singular, is

[2021]

Option A: 45/162

Option B: 23/81

Option C: 22/81

Option D: 43/162

Option D: 43/162

JEE Mains Probability Questions No: 90

A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is

[2021]

Correct Ans : 4

JEE Mains Math Probability Questions No: 91

A student appeared in an examination consisting of 8 true false type questions. The students guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least ‘n’ correct answers is less than is

[2021]

Option A: 5

Option B: 6

Option C: 3

Option D: 4

Option A: 5

Probability Questions for JEE Questions No: 92

The probability that a randomly selected 2-digit number belongs to the set (n ∈ N : (2n – 2) is a multiple of 3} is equal to

[2021]

Option A: 1/6

Option B: 2/3

Option C: 1/2

Option D: 1/3

Option C: 1/2

Probability Problems for Class 11 Questions No: 93

When a certain biased die is rolled, a particular face occurs with probability (1/6) – x and its opposite face occurs with probability (1/6) + x. All other faces occur with probability (1/6). Note that opposite faces sum to 7 in any die. If 0 < x < (1/6) , and the probability of obtaining total sum = 7, when such a die is rolled twice, is (13/96) , then the value of x is:

[2021]

Option A: 1/16

Option B: 1/8

Option C: 1/9

Option D: 1/12

Option B: 1/8

Probability Problems for Class 12 Questions No: 94

Let S = {1, 2, 3, 4, 5, 6). Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is

[2021]

Option A: 1/10

Option B: 1/15

Option C: 1/5

Option D: 1/30

Option A:  1/10

Probability Problems for Class 11 JEE Questions No: 95

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to

[2021]