Probability PYQs - Last 5 Years

JEE Main / Mathematics / Algebra / 125 recent questions

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

PYQs on Page

Mathematics / Algebra

2022-2026

Year Range

Based on indexed question metadata

125

Last 5 Years

2022-2026

125

Last 10 Years

2017-2026

Recent Year Trend

2022

2023

2024

2025

2026

202233 max PYQs/year2026

Question Types

125PYQs

MCQ79.2%

INTEGER20.8%

Difficulty Mix

#1 Medium101

#2 Easy19

#3 Hard5

125 in last 5 years125 in last 10 years

Last 5 Years Probability Questions

Showing 25 of 125 filtered questions.

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) \(-\) f(c) = f(d) is :

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. A candidate is randomly chosen from the quali...

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let \(\mathrm{X}\) be the number of white balls, among the drawn balls. If \(\sigma^{2}\) is the variance of \(\mathrm{X}\), then \(100 \sigma^{2}\) is ...

INTEGER+4 / -12022

Let \(\mathrm{A}\) and \(\mathrm{B}\) be two events such that \(P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}\) and \(P(A \cap B)=\frac{1}{9} \cdot\) Consider
(S1) \(P\left(A^{\prime} \cup B\right)=\frac{5}{6}\),
(S2) $$P\left(A^{\prime}...

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 :

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 \(({x_1} < {x_2} < {x_3} < {x_4} < {x_5})\). The probability that \({x_2} = 7\) and $${x_4} ...

Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that \(P({E_n}) = {n \over {36}}\) for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}...

INTEGER+4 / -12022

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 :

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

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

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 \(P(X>n-3)=\frac{k}{2^{n}}\), then k is equal to :

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 :

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 96 p is equal to _______________.

INTEGER+4 / -12022

Let \(\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}\) be three mutually exclusive events such that \(\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{2+3 \mathrm{p}}{6}, \mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{2-\mathrm{p}}{8}\) and $$\math...

The mean and variance of a binomial distribution are \(\alpha\) and \(\frac{\alpha}{3}\) respectively. If \(\mathrm{P}(X=1)=\frac{4}{243}\), then \(\mathrm{P}(X=4\) or 5\()\) is equal to :

Let \(X\) be a binomially distributed random variable with mean 4 and variance \(\frac{4}{3}\). Then, \(54 \,P(X \leq 2)\) is equal to :

Let E1 and E2 be two events such that the conditional probabilities \(P({E_1}|{E_2}) = {1 \over 2}\), \(P({E_2}|{E_1}) = {3 \over 4}\) and \(P({E_1} \cap {E_2}) = {1 \over 8}\). Then :

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 \({1 \over n}\). If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

If the numbers appeared on the two throws of a fair six faced die are \(\alpha\) and \(\beta\), then the probability that \(x^{2}+\alpha x+\beta>0\), for all \(x \in \mathbf{R}\), is :

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 :

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{5}\) and \(P(A \cup B)=\frac{1}{2}\), then \(P\left(A \mid B^{\prime}\right)+P\left(B \mid A^{\prime}\right)\) is equal to :

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

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 be 1 red and 1 black. If the probability that both balls come...

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 \({3 \over 4}\) and the remaining 6 questions correctly with probability \({1 \over 4}\). If the ...

INTEGER+4 / -12022

A random variable X has the following probability distribution :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidde...