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Previous year question hub

Probability - Algebra - Mathematics Previous Year Questions

Practice Probability - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

16Papers
15Years
32Questions
1Topics

Probability question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Probability. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 32 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 31 96.9%
Subjective 1 3.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
32 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
32 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Probability
32 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

WB JEE 2025
3 Qs
VITEEE 2025
1 Qs
WB JEE 2024
3 Qs
WB JEE 2023
2 Qs
WB JEE 2022
2 Qs
WB JEE 2021
1 Qs
WB JEE 2020
3 Qs
WB JEE 2019
2 Qs
WB JEE 2018
2 Qs
WB JEE 2017
1 Qs
WB JEE 2016
3 Qs
WB JEE 2012
1 Qs
WB JEE 2011
2 Qs
WB JEE 2010
2 Qs
WB JEE 2009
2 Qs
WB JEE 2008
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520251View paper
WB JEE 202520253View paper
WB JEE 202420243View paper
WB JEE 202320232View paper
WB JEE 202220222View paper
WB JEE 202120211View paper
WB JEE 202020203View paper
WB JEE 201920192View paper
WB JEE 201820182View paper
WB JEE 201720171View paper
WB JEE 201620163View paper
WB JEE 201220121View paper
WB JEE 201120112View paper
WB JEE 201020102View paper
WB JEE 200920092View paper
WB JEE 200820082View paper

All Probability previous year questions

Practice every matching question in batches of 20, with every available option.

1
2016 · Mathematics · Algebra · Probability
WB JEE 2016
Let A and B be two events such that P(A \(\cap\) B) = \({1 \over 6}\), P(A \(\cup\) B) = \({31 \over 45}\) and P(\(\overline B\)) = \({7 \over 10}\), then
A
A and B are independent
B
A and B are mutually exclusive
C
\(P\left( {{A \over B}} \right) < {1 \over 6}\)
D
\(P\left( {{B \over A}} \right) < {1 \over 6}\)
Open complete paper
2
2016 · Mathematics · Algebra · Probability
WB JEE 2016
In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is
A
\({2 \over 7}\)
B
\({1 \over 2}\)
C
\({1 \over 4}\)
D
\({5 \over 6}\)
Open complete paper
3
2016 · Mathematics · Algebra · Probability
WB JEE 2016
If A, B are two events such that P(A \(\cup\) B) \(\ge\) \({3 \over 4}\) and \({1 \over 8}\) \(\le\) P (A \(\cap\) B) \(\le\) \({3 \over 8}\), then
A
P(A) + P(B) \(\le\) \({11 \over 8}\)
B
P(A) . P(B) \(\le\) \({3 \over 8}\)
C
P(A) + P(B) \(\ge\) \({7 \over 8}\)
D
None of the above
Open complete paper
4
2017 · Mathematics · Algebra · Probability
WB JEE 2017
The probability that a non-leap year selected at random will have 53 Sunday is
A
0
B
1/7
C
2/7
D
3/7
Open complete paper
5
2018 · Mathematics · Algebra · Probability
WB JEE 2018
In order to get a head at least once with probability \(\ge\) 0.9, the minimum number of times a unbiased coin needs to be tossed is
A
3
B
4
C
5
D
6
Open complete paper
6
2018 · Mathematics · Algebra · Probability
WB JEE 2018
A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing in tests I, II and III are respectively p, q and 1/2. If the probability of the student to be successful is 1/2. Then
A
p (1 + q) = 1
B
q (1 + p) = 1
C
pq = 1
D
\({1 \over p} + {1 \over q} = 1\)
Open complete paper
7
2019 · Mathematics · Algebra · Probability
WB JEE 2019
If X is a random variable such that \(\sigma\)(X) = 2.6, then \(\sigma\)(1 \(-\) 4X) is equal to
A
7.8
B
\(-\) 10.4
C
13
D
10.4
Open complete paper
8
2019 · Mathematics · Algebra · Probability
WB JEE 2019
A problem in mathematics is given to 4 students whose chances of solving individually are \({{1 \over 2}}\), \({{1 \over 3}}\), \({{1 \over 4}}\) and \({{1 \over 5}}\). The probability that the problem will be solved at least by one student is
A
\({{2 \over 3}}\)
B
\({{3 \over 5}}\)
C
\({{4 \over 5}}\)
D
\({{3 \over 4}}\)
Open complete paper
9
2020 · Mathematics · Algebra · Probability
WB JEE 2020
Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins if A begins?
A
\({1 \over 4}\)
B
\({1 \over 2}\)
C
\({7 \over 12}\)
D
\({8 \over 15}\)
Open complete paper
10
2020 · Mathematics · Algebra · Probability
WB JEE 2020
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire to have more than 50% chance of hitting it at least once, is
A
5
B
7
C
9
D
11
Open complete paper
11
2020 · Mathematics · Algebra · Probability
WB JEE 2020
A and B are independent events. The probability that both A and B occur is \({1 \over {20}}\) and the probability that neither of them occurs is \({3 \over {5}}\). The probability of occurrence of A is
A
\({1 \over {2}}\)
B
\({1 \over {10}}\)
C
\({1 \over {4}}\)
D
\({1 \over {5}}\)
Open complete paper
12
2021 · Mathematics · Algebra · Probability
WB JEE 2021
Four persons A, B, C and D throw and unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins the game if A begins?
A
\({1 \over 4}\)
B
\({1 \over 2}\)
C
\({7 \over 15}\)
D
\({8 \over 15}\)
Open complete paper
13
2022 · Mathematics · Algebra · Probability
WB JEE 2022

A, B, C are mutually exclusive events such that \(P(A) = {{3x + 1} \over 3}\), \(P(B) = {{1 - x} \over 4}\) and \(P(C) = {{1 - 2x} \over 2}\). Then the set of possible values of x are in

A
[0, 1]
B
\(\left[ {{1 \over 3},{1 \over 2}} \right]\)
C
\(\left[ {{1 \over 3},{2 \over 3}} \right]\)
D
\(\left[ {{1 \over 3},{{13} \over 3}} \right]\)
Open complete paper
14
2022 · Mathematics · Algebra · Probability
WB JEE 2022

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

A
\({3 \over {16}}\)
B
\({3 \over 8}\)
C
\({1 \over 4}\)
D
\({5 \over 8}\)
Open complete paper
15
2023 · Mathematics · Algebra · Probability
WB JEE 2023

Let A and B are two independent events. The probability that both A and B happen is \({1 \over {12}}\) and probability that neither A and B happen is \({1 \over 2}\). Then

A
\(P(A) = {1 \over 3},P(B) = {1 \over 4}\)
B
\(P(A) = {1 \over 2},P(B) = {1 \over 6}\)
C
\(P(A) = {1 \over 6},P(B) = {1 \over 2}\)
D
\(P(A) = {2 \over 3},P(B) = {1 \over 8}\)
Open complete paper
16
2023 · Mathematics · Algebra · Probability
WB JEE 2023

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and \(\mathrm{E_k=\{(a,b)\in S:ab=k\}}\). If \(\mathrm{p_k=P(E_k)}\), then the correct among the following is :

A
\(\mathrm{p_1 < p_{10} < p_4}\)
B
\(\mathrm{p_1 < p_{8} < p_{14}}\)
C
\(\mathrm{p_1 < p_{8} < p_{17}}\)
D
\(\mathrm{p_1 < p_{16} < p_5}\)
Open complete paper
17
2024 · Mathematics · Algebra · Probability
WB JEE 2024

Two smallest squares are chosen one by one on a chess board. The probability that they have a side in common is

A
\(\frac{1}{9}\)
B
\(\frac{2}{7}\)
C
\(\frac{1}{18}\)
D
\(\frac{5}{18}\)
Open complete paper
18
2024 · Mathematics · Algebra · Probability
WB JEE 2024

Two integers \(\mathrm{r}\) and \(\mathrm{s}\) are drawn one at a time without replacement from the set \(\{1,2, \ldots, \mathrm{n}\}\). Then \(\mathrm{P}(\mathrm{r} \leq \mathrm{k} / \mathrm{s} \leq \mathrm{k})=\)

(k is an integer < n)

A
\(\frac{\mathrm{k}}{\mathrm{n}}\)
B
\(\frac{\mathrm{k}}{\mathrm{n}-1}\)
C
\(\frac{\mathrm{k}-1}{\mathrm{n}}\)
D
\(\frac{k-1}{n-1}\)
Open complete paper
19
2024 · Mathematics · Algebra · Probability
WB JEE 2024

A biased coin with probability \(\mathrm{p}(0<\mathrm{p}<1)\) of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5}\), then \(\mathrm{p}=\)

A
\(\frac{1}{4}\)
B
\(\frac{1}{3}\)
C
\(\frac{2}{3}\)
D
\(\frac{3}{4}\)
Open complete paper
20
2025 · Mathematics · Algebra · Probability
WB JEE 2025

Three numbers are chosen at random without replacement from $\{1,2, \ldots 10\}$. The probability that the minimum of the chosen numbers is 3 or their maximum is 7 , is

A
$\frac{5}{40}$
B
$\frac{3}{40}$
C
$\frac{11}{40}$
D
$\frac{9}{40}$
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Showing 20 of 32 questions