Probability is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Probability with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Probability questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
Also Read
WBJEE PYQs for Probability with Solutions
1.
An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is- $\frac{40}{143}$
- $\frac{70}{143}$
- $\frac{3}{13}$
- $\frac{10}{13}$
2.
$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3,.....,n$ and the probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$ .Now , the probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is- $\frac{2018}{2019}$
- $\frac{2018}{(2019)^2}$
- $\frac{2000}{(2019) }$
- $\frac{2000}{(2019)^2}$
3.
The value of- (A) 0
- (B)
- (C) tan-1 2
- (D)
4.
There are 7 greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,- $^{7}C_{3}$
- $2.^{7}C_{3}$
- $3! ^{4}C_{4}$
- $3! ^{7}C_{3} \, ^{4}C_{3}$
5.
If $A, B$ are two events such that $P\left(A\cup B\right) \ge \frac{3}{4}$ and $\frac{1}{8}\le P\left(A\cap B\right) \le\frac{3}{8}$ then- $P\left(A\right)+P\left(B\right)\le\frac{11}{8}$
- $P\left(A\right).P\left(B\right)\le\frac{3}{8}$
- $P\left(A\right)+P\left(B\right)\ge\frac{7}{8}$
- $None\, of \, these$
6.
The probability that a non leap year selected at random will have $53$ Sundays is- $0$
- $1/7$
- $2/7$
- $3/7$
7.
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and Ek={(a,b)∈S:ab=k}. If Pk=P(Ek), then the correct among the following is- p1<p10<p4
- p2<p8<p14
- p4<p8<p17
- p1<p10<p4
8.
Let A and B be two independent events. The probability that both A and B happens is \(\frac{1}{12}\) and the probability that neither A nor B happens is \(\frac{1}{2}\). Then- P(A)=\(\frac{1}{3}\), P(B)=\(\frac{1}{4}\)
- P(A)=\(\frac{1}{2}\), P(B)=\(\frac{1}{6}\)
- P(A)=\(\frac{1}{6}\), P(B)=\(\frac{1}{2}\)
- P(A)=\(\frac{2}{3}\), P(B)=\(\frac{1}{8}\)
9.
$A$ and $B$ are two independent events such that $P\left(A\cup B'\right)=0.8$, and $P\left(A\right)=0.3$ Then, $P(B)$ is- $\frac{2}{7}$
- $\frac{2}{3}$
- $\frac{3}{8}$
- $\frac{1}{8}$
10.
The value of cos 15° – sin 15° is- (A) 0
- (B) 1/√2
- (C)
- (D) 1/2√2
11.
Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $\frac{2}{3}$
12.
A fair six-faced die is rolled $12$ times. The probability that each face turns up twice is equal to- $\frac{12!}{6!6!6^{12}}$
- $\frac{2^{12}}{2^{6}6^{12}}$
- $\frac{12!}{2^{6}6^{12}}$
- $\frac{12!}{6^{2}6^{12}}$
13.
An objective type test paper has $5$ questions. Out of these $5$ questions, $3$ questions have four options each $(A, B, C, D)$ with one option being the correct answer. The other $2$ questions have two options each, namely True and False. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in at least four questions, is- $\frac{5}{32}$
- $\frac{3}{128}$
- $\frac{3}{256}$
- $\frac{3}{64}$
14.
A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is- Jan-64
- Jan-32
- 44577
- 44569
Comments