Probability (IPMAT/JIPMAT) - Free PYQs + Solutions

Q1:

Indore 2025

Modern Math

>

Probability

Medium

Q1:

A natural number

n

lies between

100

and

400

, and the sum of its digits is

10

. The probability that

n

is divisible by

4

, is

\frac{1}{4}

\frac{7}{27}

\frac{1}{3}

\frac{2}{9}

Explanation →

Q2:

Indore 2025

Modern Math

>

Probability

Medium

Q2:

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

\frac{1}{2}

\frac{10}{19}

\frac{2}{3}

\frac{9}{19}

Explanation →

Q3:

Indore 2023

Modern Math

>

Probability

Easy

Q3:

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is

5

6

3

7

Explanation →

Q4:

Indore 2023

Modern Math

>

Probability

Medium

Q4:

The probability that a randomly chosen positive divisor of

10 ^ {2023}

is an integer multiple of

10 ^ {2001}

is

\dfrac{22}{2023}

\dfrac{23^2}{{2024}^2}

\dfrac{22}{2024}

\dfrac{22^2}{{2023}^2}

Explanation →

Q5:

Indore 2020

Modern Math

>

Probability

Hard

Q5:

The probability that a randomly chosen factor of

10^{19}

is a multiple of

10^{15}

is

\frac{1}{25}

\frac{1}{12}

\frac{1}{20}

\frac{1}{16}

Explanation →

Q6:

Indore 2020

Modern Math

>

Probability

Hard

Q6:

A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is

\frac{4}{9}

\frac{5}{9}

\frac{4}{15}

\frac{2}{15}

Explanation →

Q7:

Indore 2019

Modern Math

>

Probability

Medium

Q7:

A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

\frac{1}{6}

\frac{1}{4}

\frac{1}{5}

\frac{1}{10}

Explanation →

Q8:

Indore 2019

Modern Math

>

Probability

Hard

Q8:

From a pack of 52 cards, we draw one by one, without replacement. If

f(n)

is the probability that an Ace will appear at the

n^{\text{th}}

turn, then

f(2) = \frac{1}{13} > f(3)

\frac{1}{13} > f(2) > f(3)

f(3) > f(2) = \frac{1}{13}

f(2) = f(3) = \frac{1}{13}

Explanation →

Q9:

JIPMAT 2025

Modern Math

>

Probability

Medium

Q9:

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, in narrating the same incident?

5%

15%

35%

45%

Explanation →

Q10:

JIPMAT 2025

Modern Math

>

Probability

Hard

Q10:

Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children is:

\frac{1}{9}

\frac{2}{9}

\frac{1}{12}

\frac{10}{21}

Explanation →

Q11:

JIPMAT 2024

Modern Math

>

Probability

Medium

Q11:

A speaks the truth in

75 \%

cases and

B

in

80 \%

of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

5 \%

15 \%

35 \%

45 \%

Explanation →

Q12:

JIPMAT 2023

Modern Math

>

Probability

Conceptual

Q12:

Let A and B be two events such that P(A)=0.25, P(B)=0.50 and P(A ∩ B)=0.14. The probability that neither A nor B occurs is:

0.09

0.19

0.39

0.29

Explanation →

Q13:

JIPMAT 2023

Modern Math

>

Probability

Easy

Q13:

The probabilities that A, B, and D can solve a problem independently are 1/3, 1/3, and 1/4 respectively. The probability that only two of them are able to solve the problem is:

\frac{5}{36}

\frac{7}{36}

\frac{13}{36}

\frac12

Explanation →

Q14:

JIPMAT 2023

Modern Math

>

Probability

Easy

Q14:

Given below are two statements in the context of throwing two different dice together:

Statement (I): The probability that the two numbers obtained have an even sum is 0.50.

Statement (II): The probability that the two numbers obtained have an even product is 0.75.

In light of the above statements, choose the most appropriate answer from the options given below.

Both Statement (I) and Statement (II) are true.

Both Statement (I) and Statement (II) are false.

Statement (I) is true but Statement (II) is false.

Statement (I) is false but Statement (II) is true.

Explanation →

Q15:

JIPMAT 2022

Modern Math

>

Probability

Medium

Q15:

Given below are two statement based on the following

If

A

and

B

are independent events such that

P(A)=p, P(B)=2 p

and

P

(exactly one of

A, B)=\frac{5}{9}

Statement I:

\mathrm{p}=\frac{1}{3}

Statement II:

\mathrm{p}=\frac{5}{12}

In the light of the above statements, choose the correct answer form the question given below

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Explanation →

Q16:

Rohtak 2019

Modern Math

>

Probability

Medium

Q16:

A bag contains 4 blue, 5 white and 6 green balls. Two balls are drawn at random. What is the probability that one ball is white?

(\frac{10}{21})

(\frac{1}{2})

(\frac{3}{4})

(\frac{2}{35})

Explanation →

Probability - Past Year Questions

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Probability - Past Year Questions (Free PDF Download)