Probability PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 206 recent questions

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

2023

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.

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 probability that exactly one of C and A occurs is (1 \(-\) k...

Let X be a random variable with 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:hidden;padding:10px 5px;w...

INTEGER+4 / -12021

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

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 getting exactly 3 successes is equal to :

Two dies 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 :

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is \(\alpha\), only E2 occurs is \(\beta\) and only E3 occurs is \(\gamma\). Let 'p' denote the probability of none of events occurs that satisfies the...

INTEGER+4 / -12021

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 \({1 \over 2}\) and probability of occurrence of 0 at the odd place be \({1 \over 3}\). Then th...

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 :

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 :

In a box, there are 20 cards, out of which 10
are lebelled as A and the remaining 10 are
labelled as B. Cards are drawn at random, one
after the other and with replacement, till a
second A-card is obtained. The probability that
the second A...

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 :

A random variable X has the following
probability distribution :

.tg {border-collapse:collapse;border-spacing:0;width:100%}
.tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:...

Let A and B be two independent events such
that P(A) = \({1 \over 3}\) and P(B) = \({1 \over 6}\). Then, which of
the following is TRUE?

Let A and B be two events such that the
probability that exactly one of them occurs is \({2 \over 5}\) and the probability that A or B occurs is \({1 \over 2}\) ,
then the probability of both of them occur
together is :

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k
consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected
value of X, is :

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is \({{1 \over 4}}\)
. If the probability that at most two machines will be out of service on the same day is $${\left( {{3 \over 4}...

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

The probabilities of three events A, B and C are
given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.
If P(A\(\cup\)B) = 0.8, P(A\(\cap\)C) = 0.3, P(A\(\cap\)B\(\cap\)C) = 0.2,
P(B\(\cap\)C) = \(\beta\) and P(A\(\cup\)B\(\cup\)C) ...

In a bombing attack, there is 50% chance that
a bomb will hit the target. Atleast two
independent hits are required to destroy the
target completely. Then the minimum number
of bombs, that must be dropped to ensure that
there is at least 99...

INTEGER+4 / -02020

The probability of a man hitting a target is \({1 \over {10}}\). The least number of shots required, so that the
probability of his hitting the target at least once is greater than \({1 \over {4}}\), is ____________.

INTEGER+4 / -02020

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 throws total a of 6 before B throws a total of 7 and B wins t...

A dice 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 atleast once is :

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

Box I contains 30 cards numbered 1 to 30 and
Box II 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 to be
a non-prime number. The probability that the
card was dr...

Let EC denote the complement of an event E.
Let E1
, E2
and E3
be any pairwise independent
events with P(E1) > 0
and P(E1 \(\cap\) E2 \(\cap\) E3) = 0.
Then P(\(E_2^C \cap E_3^C/{E_1}\)) is equal to :

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P (X = 2) equals :

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not r...

Four persons can hit a target correctly with
probabilities
\({1 \over 2}\), \({1 \over 3}\), \({1 \over 4}\) and
\({1 \over 8}\) respectively. if all hit
at the target independently, then the probability that
the target would be hit, is :

Let A and B be two non-null events such that
A \(\subset\) B . Then, which of the following statements
is always correct?

The minimum number of times one has to toss a
fair coin so that the probability of observing at least
one head is at least 90% is :

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his ...

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC
nor for NSS is :

Let a random variable X have a binomial distribution with mean 8 and variance 4. If \(P\left( {X \le 2} \right) = {k \over {{2^{16}}}}\), then k
is equal to :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle
formed with these chosen vertices is equilateral is :

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability
that the candidate solve any problem is \({4 \over 5}\)
, then the probability that he is unable to solve less than two
problems...

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins
Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the
expected gain/loss (in Rs....

Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

Let S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left( {{{mean\,\,of\,X} \over {s\tan dard\,\,deviation\,\,of\,X}}} \right...

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards nu...

If the probability of hitting a target by a shooter, in any shot, is \({1 \over 3}\), then the minimum number of independent
shots at the target required by him so that the probability of hitting the target atleast once is greater than $${5...

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,
then the conditional probability that all children are girls given that at least two are girls is :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is
more than 99% is :

Let A, B and C be three events, which are pair-wise independent and \(\overrightarrow E\) denotes the completement of an event E. If \(P\left( {A \cap B \cap C} \right) = 0\) and \(P\left( C \right) > 0,\) then $$P\left[ {\left( {\overline...

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to ...

A box 'A' contains \(2\) white, \(3\) red and \(2\) black balls. Another box 'B' contains \(4\) white, \(2\) red and \(3\) black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns ou...

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, ...

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and
this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at
random from the bag, ...

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :