Probability PYQs - Last 10 Years

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MathematicsAlgebra2017-2026

All Probability PYQs Last 5 Years Create chapter test

Practice 206 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.

206

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

125

Last 5 Years

2022-2026

206

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

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2024

2025

2026

202134 max PYQs/year2026

Question Types

206PYQs

MCQ83.5%

INTEGER16.5%

Difficulty Mix

#1 Medium157

#2 Easy43

#3 Hard6

125 in last 5 years206 in last 10 years

Last 10 Years Probability Questions

Showing 50 of 206 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 :

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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...

INTEGER+4 / -12021

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 :

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

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 probability of guessing at least 'n' correct answers is less than ...

When a certain biased die is rolled, a particular face occurs with probability \({1 \over 6} - x\) and its opposite face occurs with probability \({1 \over 6} + x\). All other faces occur with probability \({1 \over 6}\). Note that opposite...

The probability distribution of random variable X is given by :
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INTEGER+4 / -12021

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 :

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 :

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 :

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) = \({5 \over 9}\), is :

Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equationsx + y + z = 5x + 2y + 3z = \(\mu\) x + 3y + \(\lambda\)z = 1is constructed. If p is the probability that the system has a un...

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 \(\ge\) 5 | x > 2) is :

Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is \(k{\left( {{3 \over 4}} \right)^9}\) then k lies in the set :

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 ______________.

INTEGER+4 / -12021

Let X be a random variable such that the probability function of a distribution is given by \(P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )\). Then the mean of the distribution and P(X is positive and even) resp...

The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

When a missile is fired from a ship, the probability that it is intercepted is \({1 \over 3}\) and the probability that the missile hits the target, given that it is not intercepted, is \({3 \over 4}\). If three missiles are fired independe...

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 particular chest disorder are 35%, 20% and 10% respectively. A per...

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 :

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 the
probability of getting an odd number for odd number of tim...

Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is \(\alpha\), only B2 occurs is \(\beta\) and only B3 occurs is \(\gamma\). Let p be the probability that none of the events Bi occur...

INTEGER+4 / -12021

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

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 \(\times\) 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :

The probability of selecting integers a\(\in\)[\(-\) 5, 30] such that x2 + 2(a + 4)x \(-\) 5a + 64 > 0, for all x\(\in\)R, is :

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 :