Probability PYQs - Last 10 Years

JEE Advanced / Mathematics / Algebra / 29 recent questions

MathematicsAlgebra2017-2026

All Probability PYQs Last 5 Years Create chapter test

Practice 29 JEE Advanced Mathematics questions from Probability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

29

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

15

Last 5 Years

2022-2026

29

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

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2026

20215 max PYQs/year2026

Question Types

29PYQs

INTEGER48.3%

MCQ37.9%

MCQM13.8%

Difficulty Mix

#1 Medium18

#2 Hard8

#3 Easy3

15 in last 5 years29 in last 10 years

Last 10 Years Probability Questions

Showing 29 of 29 filtered questions.

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the ...

INTEGER+4 / -02026

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 chosen at random from them. Let $E_1$ be the event that the ba...

MCQM+4 / -12026

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 proportions of $2: 2: 1$, respectively. It is known that $20 \%$ ...

INTEGER+4 / -02025

Three students $S_1, S_2,$ and $S_3$ 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 problem, given that neither $S_2$ nor $S_3$ can solve t...

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 randomly one after the other without replacement. For $i=1,2,...

INTEGER+4 / -02024

Let $X$ be a random variable, and let $P(X=x)$ denote the probability that $X$ takes the value $x$. Suppose that the points $(x, P(X=x)), x=0,1,2,3,4$, lie on a fixed straight line in the $x y$-plane, and $P(X=x)=0$ for all $x \in \mathbb{R...

INTEGER+4 / -02024

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 for the remaining questions. Whenever the student knows the ans...

Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7 p$ is :

INTEGER+3 / -02023

Let $p_i$ be the probability that a randomly chosen point has $i$ many friends, $i=0,1,2,3,4$. Let $X$ be a random variable such that for $i=0,1,2,3,4$, the probability $P(X=i)=p_i$. Then the value of $7 E(X)$ is :

INTEGER+3 / -02023

Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional pro...

INTEGER+4 / -02023

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 $\frac{1}{3}$, then the probability that the experiment stops with head is :

Let $X=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}: \frac{x^2}{8}+\frac{y^2}{20}<1\right.$ and $\left.y^2<5 x\right\}$. Three distinct points $P, Q$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q$ and $R$ form a tr...

Suppose that

Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 green and 3 yellow balls, Box-IV contains 10 green, 16 orange and 6 white balls.

A ball is chosen ...

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 numbers. Let \(x\) and \(y\) denote the readings on the di...

In a study about a pandemic, data of 900 persons was collected. It was found that

190 persons had symptom of fever,

220 persons had symptom of cough,

220 persons had symptom of breathing problem,

330 persons had symptom of fever or coug...

INTEGER+3 / -02022

A number of 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 a multiple of 7. Then the value of 500p is __________.

INTEGER+4 / -02021

Let E, F and G be three events having probabilities \(P(E) = {1 \over 8}\), \(P(F) = {1 \over 6}\) and \(P(G) = {1 \over 4}\), and let P (E \(\cap\) F \(\cap\) G) = \({1 \over {10}}\). For any event H, if Hc denotes the complement, then whi...

MCQM+4 / -22021

Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chose...

INTEGER+2 / -02021

Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chose...

INTEGER+2 / -02021

Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 \(-\) S1 and F2 = F1 \(\cup\)...

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 either a prime number or a perfect square. Suppose the sum turns ...

INTEGER+4 / -02020

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 number of missiles that have to be fired so that the probability of ...

INTEGER+3 / -12020

Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are \({{2 \over 3}}\) and \({{1 \over 3}}\), respectively. Suppose \(\alpha\) is the number of heads that appear when C1 is tossed twice, indepe...

Let S be the sample space of all 3 \(\times\) 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given byE1 = {A\(\in\)S : det A = 0} andE2 = {A\(\in\)S : sum of entries of A is 7}.If a matrix is chosen at random...

INTEGER+3 / -02019

There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities \({3 \over {10}}\), \({3 \over {10}}\) and ...

MCQM+4 / -12019

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

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

Let X and Y be two events such that \(P(X) = {1 \over 3}\), \(P(X|Y) = {1 \over 2}\) and \(P(Y|X) = {2 \over 5}\). Then

MCQM+4 / -12017