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Probability

JEE Advanced · Mathematics · 58 past questions

Q1 2026 Paper 1

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green…
Q2 2026 Paper 2

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6…
Q3 2025 Paper 1

Three students $S_1, S_2$, and $S_3$ are given a problem to solve. Consider the following events…
Q4 2025 Paper 2

A factory has a total of three manufacturing units, $M_1$, $M_2$, and $M_3$, which produce bulbs independent…
Q5 2024 Paper 1

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The…
Q6 2024 Paper 1

Let $X$ be a random variable, and let $P(X = x)$ denote the probability that $X$ takes the value $x$. Suppose…
Q7 2024 Paper 2

A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue.…
Q8 2023 Paper 1

Let $X=\left\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:\frac{x^2}{8}+\frac{y^2}{20}<1\text{ and }y^2<5x\right\}$.…
Q9 2023 Paper 2

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If…
Q10 2023 Paper 2

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…
Q11 2022 Paper 1

In a study about a pandemic, data of 900 persons was collected. It was found that…
Q12 2022 Paper 1

Two players, $P_1$ and $P_2$, play a game against each other. In every round of the game, each player rolls a…
Q13 2022 Paper 2

Suppose that…
Q14 2021 Paper 1

Consider three sets $E_1 = \{1,2,3\}$, $F_1 = \{1,3,4\}$ and $G_1 = \{2,3,4,5\}$. Two elements are chosen at…
Q15 2021 Paper 1

Three numbers are chosen at random, one after another with replacement, from the set…
Q16 2021 Paper 1

Three numbers are chosen at random, one after another with replacement, from the set…
Q17 2021 Paper 1

Let $E, F$ and $G$ be three events having probabilities…
Q18 2021 Paper 2

A number is chosen at random from the set $\{1, 2, 3, \ldots, 2000\}$. Let $p$ be the probability that the…
Q19 2020 Paper 1

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting head in a single toss are…
Q20 2020 Paper 2

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely…
Q21 2020 Paper 2

Two fair dice, each with faces numbered $1,2,3,4,5$ and $6$, are rolled together and the sum of the numbers…
Q22 2019 Paper 1

There are three bags $B_1, B_2$ and $B_3$. The bag $B_1$ contains 5 red and 5 green balls, $B_2$ contains 3…
Q23 2019 Paper 1

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0,1\}$. Let the events…
Q24 2019 Paper 2

Let $|X|$ denote the number of elements in a set $X$. Let $S = \{1,2,3,4,5,6\}$ be a sample space, where each…
Q25 2018 Paper 1

PARAGRAPH “A”…
Q26 2018 Paper 1

PARAGRAPH “A”…
Q27 2017 Paper 1

Let $X$ and $Y$ be two events such that $P(X)=\frac13$, $P(X|Y)=\frac12$ and $P(Y|X)=\frac25$. Then
Q28 2017 Paper 2

Three randomly chosen nonnegative integers $x,y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then…
Q29 2016 Paper 1

A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces 20% and plant $T_2$…
Q30 2016 Paper 2

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of…
Q31 2016 Paper 2

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of…
Q32 2015 Paper 1

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two…
Q33 2015 Paper 2

PARAGRAPH 1…
Q34 2015 Paper 2

PARAGRAPH 1…
Q35 2014 Paper 2

Six cards and six envelopes are numbered $1,2,3,4,5,6$ and cards are to be placed in envelopes so that each…
Q36 2014 Paper 2

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at…
Q37 2014 Paper 2

Paragraph For Questions 55 and 56…
Q38 2014 Paper 2

Paragraph For Questions 55 and 56…
Q39 2013 Paper 1

Four persons independently solve a certain problem correctly with probabilities…
Q40 2013 Paper 1

Of the three independent events $E_1$, $E_2$ and $E_3$, the probability that only $E_1$ occurs is $\alpha$…
Q41 2013 Paper 2

Paragraph for Questions 51 and 52…
Q42 2013 Paper 2

Paragraph for Questions 51 and 52…
Q43 2012 Paper 1

A ship is fitted with three engines $E_1$, $E_2$ and $E_3$. The engines function independently of each other…
Q44 2012 Paper 2

Four fair dice $D_1, D_2, D_3$ and $D_4$, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled…
Q45 2012 Paper 2

Let $X$ and $Y$ be two events such that $P(X\mid Y)=\frac12$, $P(Y\mid X)=\frac13$ and $P(X\cap Y)=\frac16$.…
Q46 2011 Paper 1

Paragraph for Question Nos. 61 and 62…
Q47 2011 Paper 1

Paragraph for Question Nos. 61 and 62…
Q48 2011 Paper 2

Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is…
Q49 2010 Paper 1

Let $\omega$ be a complex cube root of unity with $\omega\neq1$. A fair die is thrown three times. If $r_1$…
Q50 2010 Paper 2

A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received…
Q51 2009 Paper 1

Paragraph for Question Nos. 36 to 38…
Q52 2009 Paper 1

Paragraph for Question Nos. 36 to 38…
Q53 2009 Paper 1

Paragraph for Question Nos. 36 to 38…
Q54 2008 Paper 1

Consider the system of equations $ax + by = 0$, $cx + dy = 0$, where $a, b, c, d \in \{0, 1\}$.…
Q55 2008 Paper 2

An experiment has 10 equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If…
Q56 2007 Paper 1

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the…
Q57 2007 Paper 1

Let $H_1, H_2, \ldots, H_n$ be mutually exclusive and exhaustive events with $P(H_i) > 0$…
Q58 2007 Paper 2

Let $E^c$ denote the complement of an event $E$. Let $E, F, G$ be pairwise independent events with $P(G) > 0$…