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JEE Probability PYQs with Solutions

561 previous year questions from Probability (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

561 questionsMathematics2006–2026Answers + solutions

About Probability PYQs

Probability has 561 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (165) and JEE Advanced (55), spanning 2006 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 18
  • 2025: 25
  • 2024: 25
  • 2023: 30
  • 2022: 31
  • 2021: 37
  • 2020: 17
  • 2019: 3
  • 2018: 2
  • 2017: 2
  • 2016: 3
  • 2015: 3

Probability questions with solutions

1

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is

JEE Advanced 2026 Solution View → 2

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and

JEE Main 2026 Solution View → 3

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one

JEE Main 2026 Solution View → 4

A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is (9)/(16) , then

JEE Main 2026 Solution View → 5

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If A is selected the captain, the probability that

JEE Main 2026 Solution View → 6

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came

JEE Main 2026 Solution View → 7

From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to (a)/(b) , where a,b ∈ ℕ and (a,b)=1

JEE Main 2026 Solution View → 8

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p , then 96p is equal to

JEE Main 2026 Solution View → 9

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is (m)/(n)

JEE Main 2026 Solution View → 10

The probability distribution of a random variable X is given below : \( array |c|c|c|c|c|c|c|c|c| X & 4k & (30)/(7) k& (32)/(7)k & (34)/(7) k& (36)/(7)k & (38)/(7) k& (40)/(7)k &

JEE Main 2026 Solution View → 11

A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10 . If three balls are drawn at random without replacement and all of them are found to be

JEE Main 2026 Solution View → 12

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair ( A, B ) from the set P(S) × P(S) such that A ∩ B=∅ . If the

JEE Main 2026 Solution View → 13

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is

JEE Main 2026 Solution View → 14

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A.

JEE Main 2026 Solution View → 15

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a-b 10 is (m)/(n), gcd(m, n)=1 , then m+n is

JEE Main 2026 Solution View → 16

If a random variable x has the probability distribution array |c|c|c|c|c|c|c|c|c| x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 P(x) & 0 & 2k & k & 3k & 2k^ 2 & 2k & k^ 2 +k & 7k^ 2 array

JEE Main 2026 Solution View → 17

Two distinct numbers a and b are selected at random from 1,2,3, …, 50 . The probability, that their product a b is divisible by 3, is

JEE Main 2026 Solution View → 18

A random variable X takes values 0,1,2,3 with probabilities (2 a+1)/(30), (8 a-1)/(30), (4 a+1)/(30), b respectively, where a, b ∈ R . Let μ and σ respectively be the mean and

JEE Main 2026 Solution View → 19

Three students S_1, S_2 and S_1 are given a problem to solve. Consider the following events : U: At least one of S_1, S_2 and S_3 can solve the problem, V: S_1 can solve the

JEE Advanced 2025 Solution View → 20

A factory has a total of three manufacturing units, M_1, M_2 , and M_3 , which produce bulbs independent of each other. The units M_1, M_2 , and M_3 produce bulbs in the

JEE Advanced 2025 Solution View → 21

If A and B are two events such that P(A)=0.7 , P(B)=0.4 and P(A ∩ B )=0.5 , where B denotes the complement of B , then P(B (A ∪ B )) is equal:-

JEE Main 2025 Solution View → 22

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased

JEE Main 2025 Solution View → 23

Let a random variable X take values 0,1,2,3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X^2)=2 E(X) . Then the value of 8 p-1 is :

JEE Main 2025 Solution View → 24

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is (11)/(50)

JEE Main 2025 Solution View → 25

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:

JEE Main 2025 Solution View → 26

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

JEE Main 2025 Solution View → 27

If the probability that the random variable X takes the value x is given by P(X=x)=k(x+1) 3^ -x , x=0,1,2,3 … … , where k is a constant, then P(X ≥ 3) is equal to

JEE Main 2025 Solution View → 28

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by W_n

JEE Main 2025 Solution View → 29

Given three indentical bags each containing 10 balls, whose colours are as follows : array cccc & Red & Blue & Green Bag I & 3 & 2 & 5 Bag II & 4 & 3 & 3 Bag III & 5 & 1 & 4 array

JEE Main 2025 Solution View → 30

Three distinct numbers are selected randomly from the set \ 1,2,3, … …, 40\ . If the probability, that the selected numbers are in an increasing G.P. is (m)/(n) , gcd(m, n)=1

JEE Main 2025 Solution View → 31

Let A=[a_ i j ] be a 2 × 2 matrix such that a_ i j ∈\ 0,1\ for all i and j . Let the random variable X denote the possible values of the determinant of the matrix A . Then, the

JEE Main 2025 Solution View → 32

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then

JEE Main 2025 Solution View → 33

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the

JEE Main 2025 Solution View → 34

Bag B_1 contains 6 white and 4 blue balls, Bag B_2 contains 4 white and 6 blue balls, and Bag B_3 contains 5 white and 5 blue balls. One of the bags is selected at random and a

JEE Main 2025 Solution View → 35

Two number k_1 and k_2 are randomly chosen from the set of natural numbers. Then, the probability that the value of i^ k_1 +i^ k_2 ,(i= -1 ) is non-zero, equals

JEE Main 2025 Solution View → 36

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from

JEE Main 2025 Solution View → 37

Let A=[a_ i j ] be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P(E) is :

JEE Main 2025 Solution View → 38

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8 , and B wins if he throws a sum of 8 before A throws a sum of 5 . The

JEE Main 2025 Solution View → 39

A board has 16 squares as shown in the figure: Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

JEE Main 2025 Solution View → 40

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one

JEE Main 2025 Solution View → 41

If A and B are two events such that P(A ∩ B)=0.1 , and P(A B) and P(B A) are the roots of the equation 12 x^2-7 x+1=0 , then the value of P( A ∪ B ) P( A ∩ B ) is :

JEE Main 2025 Solution View → 42

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given

JEE Main 2025 Solution View → 43

A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ^2 denote the mean and variance of X , then the value of 64(μ+σ^2) is :

JEE Main 2025 Solution View → 44

A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn

JEE Advanced 2024 Solution View → 45

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers

JEE Advanced 2024 Solution View → 46

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i^ th roll than the number obtained in the (i-1)^ th roll, i=2,3 , is equal to

JEE Main 2024 Solution View → 47

Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,4 . If the probability that a x^2+b x+c=0 has all real

JEE Main 2024 Solution View → 48

There are three bags X, Y and Z . Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee

JEE Main 2024 Solution View → 49

Let the sum of two positive integers be 24 . If the probability, that their product is not less than (3)/(4) times their greatest possible product, is (m)/(n) , where gcd(m, n)=1

JEE Main 2024 Solution View → 50

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and yellow balls. If X and

JEE Main 2024 Solution View → 51

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:

JEE Main 2024 Solution View → 52

From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in

JEE Main 2024 Solution View → 53

A company has two plants A and B to manufacture motorcycles. 60 \% motorcycles are manufactured at plant A and the remaining are manufactured at plant B .80 \% of the motorcycles

JEE Main 2024 Solution View → 54

The coefficients a, b, c in the quadratic equation a x^2+b x+c=0 are from the set \ 1,2,3,4,5,6\ . If the probability of this equation having one real root bigger than the other

JEE Main 2024 Solution View → 55

The coefficients a, b, c in the quadratic equation a x^2+b x+c=0 are chosen from the set \ 1,2,3,4,5,6,7,8\ . The probability of this equation having repeated roots is :

JEE Main 2024 Solution View → 56

In a tournament, a team plays 10 matches with probabilities of winning and losing each match as (1)/(3) and (2)/(3) respectively. Let x be the number of matches that the team

JEE Main 2024 Solution View → 57

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball

JEE Main 2024 Solution View → 58

Let Ajay will not appear in JEE exam with probability p = (2)/(7), while both Ajay and Vijay will appear in the exam with probability q = (1)/(5) . Then the probability, that Ajay

JEE Main 2024 Solution View → 59

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are

JEE Main 2024 Solution View → 60

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

JEE Main 2024 Solution View → 61

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability

JEE Main 2024 Solution View → 62

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

JEE Main 2024 Solution View → 63

Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from

JEE Main 2024 Solution View → 64

Two integers xandy are chosen with replacement from the set 0, 1, 2, 3, … . . , 10 . Then the probability that | x - y | > 5 is :

JEE Main 2024 Solution View → 65

An integer is chosen at random from the integers 1, 2, 3, . . . . . , 50 . The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is

JEE Main 2024 Solution View → 66

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

JEE Main 2024 Solution View → 67

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second

JEE Main 2024 Solution View → 68

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a = P ( X = 3 ) , b = P ( X ≥ 3 ) and c = P ( X ≥ 6 ∣ X > 3 ) . Then (b

JEE Main 2024 Solution View → 69

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is (1)/(3) , then

JEE Advanced 2023 Solution View → 70

Consider the 6 × 6 square in the figure. Let A _ 1 , A _ 2 , … , A _ 49 be the points of intersections (dots in the picture) in some order. We say that A _ i and A _ j are friends

JEE Advanced 2023 Solution View → 71

Let X = \ (x, y) ∈ ℤ × ℤ: x ^ 2 8 + y ^ 2 20 < 1and y ^ 2 < 5x\ . Three distinct point P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle

JEE Advanced 2023 Solution View → 72

A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability

JEE Main 2023 Solution View → 73

The random variable X follows binomial distribution B ( n, p ) , for which the difference of the mean and the variance is 1 . If 2P ( X = 2 ) = 3P ( X = 1 ) , then n ^ 2 P ( X > 1

JEE Main 2023 Solution View → 74

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then

JEE Main 2023 Solution View → 75

Two dice A and B are rolled. Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is (p)/(q), where p and q are co-prime, then the sum of the

JEE Main 2023 Solution View → 76

A fair n(n > 1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is (n)/(9) , then n is equal to

JEE Main 2023 Solution View → 77

Let the probability of getting head for a biased coin be (1)/(4) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that

JEE Main 2023 Solution View → 78

Let S = \ M = [ a _ ij ], a _ ij ∈ \ 0, 1, 2\ , \ 1 ≤ i, j ≤ 2\ \ be a sample space and A\ M ∈ S: Mis invertible\ be an even. Then P(A) is equal to

JEE Main 2023 Solution View → 79

Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting

JEE Main 2023 Solution View → 80

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2 ^ N < N ! is (m)/(n) where m and n are coprime, then 4m - 3n is equal to

JEE Main 2023 Solution View → 81

If the probability that the random variable X takes values x is given by P ( X = x ) = k ( x + 1 ) 3 ^ - x , x = 0, 1, 2, 3, … … , where k is a constant, then P ( X ≥ 2 ) is equal

JEE Main 2023 Solution View → 82

In a bolt factory, machines A, B and C manufacture respectively 20 % , 30 % and 50 % of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A

JEE Main 2023 Solution View → 83

Three dice are rolled. If the probability of getting different numbers on the three dice is (p)/(q), where p and q are co-prime, then q - p is equal to

JEE Main 2023 Solution View → 84

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is k 3 ^ 11 , then k is equal to

JEE Main 2023 Solution View → 85

Two dice are thrown independently. Let A be the event that the number appeared on the 1 ^ st die is less than the number appeared on the 2 ^ nd die, B be the event that the number

JEE Main 2023 Solution View → 86

In a binomial distribution B ( n, p ) , the sum and product of the mean & variance are 5 and 6 respectively, then find 6 ( n + p - q ) is equal to :-

JEE Main 2023 Solution View → 87

Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space [0, 60] is less than or equal to a . If P(A) = (11)/(36) , then a is

JEE Main 2023 Solution View → 88

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

JEE Main 2023 Solution View → 89

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p . Next four

JEE Main 2023 Solution View → 90

If an unbiased die, marked with - 2, - 1, 0, 1, 2, 3 on its faces is thrown five times, then the probability that the product of the outcomes is positive, is :

JEE Main 2023 Solution View → 91

Let S = \ w _ 1 , w _ 2 , … .\ be the sample space associated to a random experiment. Let P( w _ n ) = P( w _ n - 1 ) 2 , n ≥ 2 . Let A = \ 2k + 3l; k, l ∈ ℕ\ and B = \ w _ n ; n

JEE Main 2023 Solution View → 92

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at

JEE Main 2023 Solution View → 93

There 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

JEE Main 2023 Solution View → 94

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

JEE Main 2023 Solution View → 95

25 % of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that

JEE Main 2023 Solution View → 96

Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S = \ x ∈ Z: x ( 66 - x ) ≥ (5)/(9)M\ and the event A = x ∈ S: x is

JEE Main 2023 Solution View → 97

The urns A, B and C contains 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

JEE Main 2023 Solution View → 98

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

JEE Main 2023 Solution View → 99

Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-ll contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 green and 3 yellow balls, Box-IV

JEE Advanced 2022 Solution View → 100

Two players, P _ 1 and P _ 2 , play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct

JEE Advanced 2022 Solution View → 101

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag

JEE Main 2022 Solution View → 102

The sum and product of the mean and variance of a binomial distribution are 82 . 5 and 1350 respectively. They the number of trials in the binomial distribution is

JEE Main 2022 Solution View → 103

Let S = \ 1, 2, 3, … , 2022\ . Then the probability, that a randomly chosen number n from the set S such that HCF(n, 2022) = 1 , is

JEE Main 2022 Solution View → 104

Let A and B be two events such that P(B ∣ A) = (2)/(5) , P(A ∣ B) = (1)/(7) and P(A ∩ B) = (1)/(9) . Consider (S1)P( A ^ ' ∪ B) = (5)/(6) , (S2)P( A ^ ' ∩ B ^ ' ) = (1)/(18) . Then

JEE Main 2022 Solution View → 105

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ ^ 2 is the variance of X

JEE Main 2022 Solution View → 106

Out of 60 % female and 40 % male candidates appearing in an exam, 60 % candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it.

JEE Main 2022 Solution View → 107

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If P(X > n - 3) = k 2 ^ n , then k is equal

JEE Main 2022 Solution View → 108

A six faced die is biased such that 3 × P (a prime number) = 6 × P (a composite number) = 2 × P(1) . Let X be a random variable that counts the number of times one gets a perfect

JEE Main 2022 Solution View → 109

Let S be the sample space of all five digit numbers. If p is the probability that a randomly selected number from S , is a multiple of 7 but not divisible by 5 , then 9p is equal

JEE Main 2022 Solution View → 110

Let X be a binomially distributed random variable with mean 4 and variance (4)/(3) . Then 54P(X ≤ 2) is equal to

JEE Main 2022 Solution View → 111

The mean and variance of a binomial distribution are α and (α)/(3) respectively. If P(X = 1) = (4)/(243) , then P(X = 4or5) is equal to:

JEE Main 2022 Solution View → 112

Let E _ 1 , E _ 2 , E _ 3 be three mutually exclusive events such that P( E _ 1 ) = (2 + 3p)/(6), P( E _ 2 ) = (2 - p)/(8) and P( E _ 3 ) = (1 - p)/(2) . If the maximum and

JEE Main 2022 Solution View → 113

If A and B are two events such that P(A) = (1)/(3), P(B) = (1)/(5) and P(A ∪ B) = (1)/(2) , then P(A B ^ ' ) + P(B A ^ ' ) is equal to

JEE Main 2022 Solution View → 114

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

JEE Main 2022 Solution View → 115

If the numbers appeared on the two throws of a fair six faced die are α and β , then the probability that x ^ 2 + + β > 0 , for all x ∈ R , is

JEE Main 2022 Solution View → 116

The probability that a relation R from \ x, y\ to \ x, y\ is both symmetric and transitive, is equal to:

JEE Main 2022 Solution View → 117

The probability, that in a randomly selected 3 -digit number at least two digits are odd, is

JEE Main 2022 Solution View → 118

If a point A(x, y) lies in the region bounded by the y -axis, straight lines 2y + x = 6 and 5x - 6y = 30 , then the probability that y < 1 is

JEE Main 2022 Solution View → 119

Let S = \ E, E _ 2 … E _ 8 \ be a sample space of raddom experiment such that P( E _ n ) = (n)/(36) for every n = 1, 2 … . 8 . Then the number of elements in the set \ A ⊂ S: P(A)

JEE Main 2022 Solution View → 120

Five numbers x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 are randomly selected from the numbers 1, 2, 3, … … , 18 and are arranged in the increasing order ( x _ 1 < x _ 2 < x _ 1 < x _

JEE Main 2022 Solution View → 121

Let X be a random variable having binomial distribution B(7, p) . If P(X = 3) = 5P(X = 4) , then the sum of the mean and the variance of X is

JEE Main 2022 Solution View → 122

If the probability that a randomly chosen 6 -digit number formed by using digits 1 and 8 only is a multiple of 21 is p , then 96p is equal to _____.

JEE Main 2022 Solution View → 123

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is

JEE Main 2022 Solution View → 124

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is (1)/(n) . If the die is thrown thrice, then the

JEE Main 2022 Solution View → 125

Let E _ 1 and E _ 2 be two events such that the conditional probabilities P( E _ 1 ∣ E _ 2 ) = (1)/(2) , P( E _ 2 ∣ E _ 1 ) = (3)/(4) and P( E _ 1 ∩ E _ 2 ) = (1)/(8) . Then

JEE Main 2022 Solution View → 126

A random variable X has the following probability distribution: X 0 1 2 3 4 P(X) k 2k 4k 6k 8k The value of P( 1

JEE Main 2022 Solution View → 127

In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability (3)/(4) and the remaining 6

JEE Main 2022 Solution View → 128

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random are found to

JEE Main 2022 Solution View → 129

If a random variable X follows the Binomial distribution B(33, p) such that 3P(X = 0) = P(X = 1) , then the value of (P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17)) is equal to

JEE Main 2022 Solution View → 130

A number is chosen at random from the set \ 1, 2, 3, … , 2000\ . Let p be the probability that the chosen number is a multiple of 3 or 7 . Then the value of 500p is ____.

JEE Advanced 2021 Solution View → 131

Consider three sets E _ 1 = 1, 2, 3 , F _ 1 = 1, 3, 4 and G _ 1 = 2, 3, 4, 5 . Two elements are chosen at random, without replacement, from the set E _ 1 , and let S _ 1 denote

JEE Advanced 2021 Solution View → 132

Three numbers are chosen at random, one after another with replacement, from the set S=\ 1,2,3, …, 100\ . Let p_ 1 be the probability that the maximum of chosen numbers is at

JEE Advanced 2021 Solution View → 133

Three numbers are chosen at random, one after another with replacement, from the set S=\ 1,2,3, …, 100\ . Let p_ 1 be the probability that the maximum of chosen numbers is at

JEE Advanced 2021 Solution View → 134

Let E, F and G be three events having probabilities P ( E ) = (1)/(8), P ( F ) = (1)/(6) and P ( G ) = (1)/(4), and let P ( E ∩ F ∩ G ) = (1)/(10) For any event H , if H ^ c

JEE Advanced 2021 Solution View → 135

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

JEE Main 2021 Solution View → 136

Let X be a random variable with distribution. x - 2 - 1 3 4 6 P ( X = x ) (1)/(5) a (1)/(3) (1)/(5) b If the mean of X is 2 . 3 and variance of X is σ ^ 2 , then 100 σ ^ 2 is

JEE Main 2021 Solution View → 137

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 :

JEE Main 2021 Solution View → 138

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

JEE Main 2021 Solution View → 139

Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is:

JEE Main 2021 Solution View → 140

The probability distribution of random variable X is given by: X 1 2 3 4 5 P ( X ) K 2K 2K 3K K Let p = P ( 1

JEE Main 2021 Solution View → 141

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

JEE Main 2021 Solution View → 142

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 :

JEE Main 2021 Solution View → 143

Let A and B be independent events such that P ( A ) = p, P ( B ) = 2p . The largest value of p , for which P (exactly one of A, B occurs) = (5)/(9) , is:

JEE Main 2021 Solution View → 144

A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the

JEE Main 2021 Solution View → 145

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

JEE Main 2021 Solution View → 146

Let X be a random variable such that the probability function of a distribution is given by P(X = 0) = (1)/(2), P(X = j) = 1 3 ^ j (j = 1, 2, 3, … , ∞) . Then the mean of the

JEE Main 2021 Solution View → 147

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 _______.

JEE Main 2021 Solution View → 148

Let 9 distinct balls be distributed among 4 boxes, B _ 1 , B _ 2 , B _ 3 and B _ 4 . If the probability that B _ 3 contains exactly 3 balls is k ((3)/(4)) ^ 9 then k lies in the

JEE Main 2021 Solution View → 149

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 entries and

JEE Main 2021 Solution View → 150

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

JEE Main 2021 Solution View → 151

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:

JEE Main 2021 Solution View → 152

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

JEE Main 2021 Solution View → 153

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

JEE Main 2021 Solution View → 154

Two dices are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:

JEE Main 2021 Solution View → 155

Let there be three independent events E _ 1 , E _ 2 and E _ 3 . The probability that only E _ 1 occurs is α only E _ 2 occurs is β and only E _ 3 occurs is γ . Let p ' ' denote

JEE Main 2021 Solution View → 156

Let A denote the event that a 6 -digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3 . Then probability of event A is equal to :

JEE Main 2021 Solution View → 157

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 :

JEE Main 2021 Solution View → 158

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

JEE Main 2021 Solution View → 159

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

JEE Main 2021 Solution View → 160

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a

JEE Main 2021 Solution View → 161

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:

JEE Main 2021 Solution View → 162

The coefficients a, b and c of the quadratic equation, a x ^ 2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is:

JEE Main 2021 Solution View → 163

When a missile is fired from 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

JEE Main 2021 Solution View → 164

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

JEE Main 2021 Solution View → 165

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then

JEE Main 2021 Solution View → 166

Let B _ i (i = 1, 2, 3) be three independent events in a sample space. The probability that only B _ 1 occur is α, only B _ 2 occurs is β and only B _ 3 occurs is γ . Let p be the

JEE Main 2021 Solution View → 167

The probability that a missile hits a target successfully is 0 . 75 . In order to destroy the target completely, at least three successful hits are required. Then the minimum

JEE Advanced 2020 Solution View → 168

Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6 , are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is

JEE Advanced 2020 Solution View → 169

Let C _ 1 and C _ 2 be two biased coins such that the probabilities of getting head in a single toss are (2)/(3) and (1)/(3) , respectively. Suppose α is the number of heads that

JEE Advanced 2020 Solution View → 170

The probabilities of three events A, B and C are given P(A) = 0 . 6, P(B) = 0 . 4 and P(C) = 0 . 5 . If P(A ∪ B) = 0 . 8, P(A ∩ C) = 0 . 3, P(A ∩ B ∩ C) = 0 . 2, P(B ∩ C) = β and

JEE Main 2020 Solution View → 171

Out of 11 consecutive natural number if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference is :

JEE Main 2020 Solution View → 172

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

JEE Main 2020 Solution View → 173

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

JEE Main 2020 Solution View → 174

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

JEE Main 2020 Solution View → 175

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

JEE Main 2020 Solution View → 176

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

JEE Main 2020 Solution View → 177

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 at

JEE Main 2020 Solution View → 178

Let E ^ C denote the complement of an event E . Let E _ 1 , E _ 2 and E _ 3 be any pairwise independent events with P( E _ 1 ) > 0 and P( E _ 1 ∩ E _ 2 ∩ E _ 3 ) = 0 then P(( E _

JEE Main 2020 Solution View → 179

Box 1 contains 30 cards numbered 1 to 30 and Box 2 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

JEE Main 2020 Solution View → 180

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is:

JEE Main 2020 Solution View → 181

A random variable X has the following probability distribution: array ll X: 1 2 3 4 5 array P(X): cases k ^ 2 & 2k k 2k 5 k ^ 2 cases Then, P(X > 2) is equal to:

JEE Main 2020 Solution View → 182

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

JEE Main 2020 Solution View → 183

Let A and B , be two events such that the probability that exactly one of them occurs is (2)/(5) , and the probability that A or B , occurs is (1)/(2) , then the probability of

JEE Main 2020 Solution View → 184

Let |X| denote the number of elements in set X . Let S = \ 1, 2, 3, 4, 5, 6\ be a sample space, where each element is equally likely to occur. If A and B are independent events

JEE Advanced 2019 Solution View → 185

There are three bags B _ 1 , B _ 2 and B _ 3 . The bag B _ 1 contains 5 red and 5 green balls, B _ 2 contains 3 red and 5 green balls, and B _ 3 contains 5 red and 3 green balls

JEE Advanced 2019 Solution View → 186

Let S be the sample space of all 3 × 3 matrices with entries from the set \ 0, 1\ . Let the events E _ 1 and E _ 2 be given by E _ 1 = \ A ∈ S: detA = 0\ and E _ 2 = A ∈ S: sum of

JEE Advanced 2019 Solution View → 187

Paragraph: There are five students S _ 1 , S _ 2 , S _ 3 , S _ 4 and S _ 5 in a music class and for them there are five seats R _ 1 , R _ 2 , R _ 3 , R _ 4 and R _ 5 arranged in a

JEE Advanced 2018 Solution View → 188

Paragraph: There are five students S _ 1 , S _ 2 , S _ 3 , S _ 4 and S _ 5 in a music class and for them there are five seats R _ 1 , R _ 2 , R _ 3 , R _ 4 and R _ 5 arranged in a

JEE Advanced 2018 Solution View → 189

Three randomly chosen non negative integers x, y, z are found to satisfy the equation x + y + z = 10 . Then the probability that z is even, is

JEE Advanced 2017 Solution View → 190

Let X and Y be two events such that P(X) = (1)/(3) , P(XY) = (1)/(2) and P(Y | X) = (2)/(5) . Then

JEE Advanced 2017 Solution View → 191

Paragraph: Football teams T_ 1 and T_ 2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_ 1

JEE Advanced 2016 Solution View → 192

Paragraph: Football teams T_ 1 and T_ 2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_ 1

JEE Advanced 2016 Solution View → 193

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

JEE Advanced 2016 Solution View → 194

Let n _ 1 and n _ 2 be the number of red and black balls, respectively, in box I. Let n _ 3 and n _ 4 be the number of red and black balls, respectively, in box II. One of the two

JEE Advanced 2015 Solution View → 195

Let n _ 1 and n _ 2 be the number of red and black balls, respectively, in box I. Let n _ 3 and n _ 4 be the number of red and black balls, respectively, in box II. A ball is

JEE Advanced 2015 Solution View → 196

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least 0 . 96 , is

JEE Advanced 2015 Solution View → 197

Paragraph: Box 1 contains three cards bearing numbers 1,2,3 ; box 2 contains five cards bearing numbers 1,2,3,4,5 ; and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7 .

JEE Advanced 2014 Solution View → 198

Paragraph: 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

JEE Advanced 2013 Solution View → 199

Paragraph: 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

JEE Advanced 2013 Solution View → 200

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

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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Probability in other exams

NDA Probability (201)BITSAT Probability (44)