Probability PYQs - Last 5 Years

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MathematicsAlgebra2022-2026

All Probability PYQs Last 10 Years Create chapter test

Practice 125 JEE Main Mathematics questions from Probability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

125

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Mathematics / Algebra

2022-2026

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125

Last 5 Years

2022-2026

125

Last 10 Years

2017-2026

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125PYQs

MCQ79.2%

INTEGER20.8%

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#1 Medium101

#2 Easy19

#3 Hard5

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Last 5 Years Probability Questions

Showing 50 of 125 filtered questions.

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 drawn is black, then the probability that it is drawn from ur...

If the mean of the following probability distribution of a radam variable \(\mathrm{X}\) :

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In a tournament, a team plays 10 matches with probabilities of winning and losing each match as \(\frac{1}{3}\) and \(\frac{2}{3}\) respectively. Let \(x\) be the number of matches that the team wins, and $y$ be the number of matches that t...

INTEGER+4 / -12024

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, that first drawn marble is red and second drawn marble is white...

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

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

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16...

INTEGER+4 / -12024

Two integers \(x\) and \(y\) are chosen with replacement from the set \(\{0,1,2,3, \ldots, 10\}\). Then the probability that \(|x-y|>5\), is :

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 the bag A, if the ball drawn is white, is

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

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

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let $a=P(X=3), b=P(X \geqslant 3)$ and $c=P(X \geqslant 6 \mid X>3)$. Then $\frac{b+c}{a}$ is equal to __________.

INTEGER+4 / -12024

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 draw gives all black balls, is :

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 black. The probability that the bag contains equal number of whit...

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay w...

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 bolt is drawn at random from the product. If t...

If the probability that the random variable \(\mathrm{X}\) takes values \(x\) is given by \(\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots\), where \(\mathrm{k}\) is a constant, then \(\mathrm{P}(\mathrm{X} \geq 2)\) is ...

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 \(\frac{k}{3^{11}}\), then \(k\) is equal to :

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

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 :

Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a . If $\mathrm{P}(\mathrm{A})=\frac{11}{36}$, then $\mathrm{a}$ is equal to _______.

INTEGER+4 / -12023

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 :

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 balls are drawn in succession with replacement and the probability...

INTEGER+4 / -12023

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 least 3 players pick the correct T-shirt is :

Let \(\mathrm{S} = \{ {w_1},{w_2},......\}\) be the sample space associated to a random experiment. Let \(P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2\). Let \(A = \{ 2k + 3l:k,l \in N\}\) and \(B = \{ {w_n}:n \in A\}\). Then P(B) is eq...

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space \(S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}\) and the event $$\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,...

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 this person is a smoker is \(\frac{k}{10}%\). Then the value of ...

INTEGER+4 / -12023

Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that \(N-2,\sqrt{3N},N+2\) are in geometric progression be \(\frac{k}{48}\). Then the value of k is :

Let \(\Omega\) be the sample space and \(\mathrm{A \subseteq \Omega}\) be an event.
Given below are two statements :
(S1) : If P(A) = 0, then A = \(\phi\)
(S2) : If P(A) = 1, then A = \(\Omega\)
Then :

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
\(x + y + z = 1\)
\(2x + \mathrm{N}y + 2z = 2\)
\(3x + 3y + \mathrm{N}z = 3\)
has unique solution is \({k \over 6}\), then the ...

Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and \(\lambda\) 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 drawn from urn...

INTEGER+4 / -12023

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

Two dice are thrown independently. Let \(\mathrm{A}\) be the event that the number appeared on the \(1^{\text {st }}\) die is less than the number appeared on the \(2^{\text {nd }}\) die, \(\mathrm{B}\) be the event that the number appeared...

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 that all the balls drawn are white is :

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 \(\mathrm{X}\) denotes the number of tosses of the coin, then the mean of \(\mathrm{X}\) is :

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

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 \(\frac{n}{9}\), then \(n\) is equal to ____________.

INTEGER+4 / -12023

Two dice A and B are rolled. Let the numbers obtained on A and B be \(\alpha\) and \(\beta\) respectively. If the variance of \(\alpha-\beta\) is \(\frac{p}{q}\), where \(p\) and \(q\) are co-prime, then the sum of the positive divisors of...

Let \(S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}\) be a sample space and \(A=\{M \in S: M\) is invertible \(\}\) be an event. Then \(P(A)\) is equal to :

Let the probability of getting head for a biased coin be \(\frac{1}{4}\). It is tossed repeatedly until a head appears. Let \(\mathrm{N}\) be the number of tosses required. If the probability that the equation $$64 \mathrm{x}^{2}+5 \mathrm{...

INTEGER+4 / -12023

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

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 even numbers twice is \(\frac{k}{2^{15}}\), then $$\mathrm...

The probability distribution of X is :

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INTEGER+4 / -12022

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then \({{P(X = 2)} \over {P(X = 3)}}\) is equal to :

The probability that a randomly chosen 2 \(\times\) 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

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

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

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.

INTEGER+4 / -12022

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 drawn from Bag II. The ball so drawn is found to be black in colour. Then ...

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