MHT CET PYQs for Probability with Solutions: Practice MHT CET Previous Year Questions

Educational Content Expert | Updated on - Nov 26, 2025

Probability is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.

This article gives you a full set of MHT CET PYQs for Probability with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Probability questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.

MHT CET PYQs for Probability with Solutions

1.
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?
- \( \frac{5}{20} \)
- \( \frac{7}{20} \)
- \( \frac{12}{20} \)
- \( \frac{5}{10} \)
View Solution
2.
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?
- \( 0.68 \)
- \( 0.95 \)
- \( 0.34 \)
- \( 0.99 \)
View Solution
3.
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).
- \( \frac{4}{15} \)
- \( \frac{4}{5} \)
- \( \frac{3}{8} \)
- \( \frac{2}{5} \)
View Solution
4.
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
- \( \frac{7}{11} \)
- \( \frac{8}{11} \)
- \( \frac{9}{11} \)
- \( \frac{10}{11} \)
View Solution
5.
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?
- \( \frac{5}{28} \)
- \( \frac{5}{21} \)
- \( \frac{3}{14} \)
- \( \frac{1}{3} \)
View Solution
6.
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.
- \( \frac{1}{6} \)
- \( \frac{5}{6} \)
- \( \binom{6}{5} \left( \frac{1}{6} \right)^5 \left( \frac{5}{6} \right) \)
- \( \frac{5}{36} \)
View Solution
7.
A die is rolled once. What is the probability of rolling a number greater than 4?
- \( \frac{1}{6} \)
- \( \frac{2}{3} \)
- \( \frac{1}{3} \)
- \( \frac{5}{6} \)
View Solution
8.
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]
- \(0.14\)
- \(0.85\)
- \(0.37\)
- \(0.23\)
View Solution
9.
If two dice are rolled, what is the probability of getting a sum of 7?
- \( \frac{1}{6} \)
- \( \frac{1}{36} \)
- \( \frac{5}{36} \)
- \( \frac{1}{3} \)
View Solution
10.
The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:
- \( \frac{n+1}{3} \)
- \( \frac{2n+1}{3} \)
- \( \frac{n+2}{3} \)
- \( \frac{2n-1}{2} \)
View Solution
11.
If a random variable X has the following probability distribution values:
X 0 1 2 3 4 5 6 7
P(X) 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
Then P(X ≥ 6) has the value:
- \( \frac{16}{100} \)
- \( \frac{81}{100} \)
- \( \frac{1}{100} \)
- \( \frac{91}{100} \)
View Solution
12.
A die is rolled. What is the probability of getting a number less than or equal to 4?
- \( \frac{2}{3} \)
- \( \frac{1}{2} \)
- \( \frac{3}{6} \)
- \( \frac{1}{3} \)
View Solution
13.
Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:
Find the mean and standard deviation.
- Mean = 2.7, Standard Deviation = 1.5
- Mean = 2.5, Standard Deviation = 1.2
- Mean = 2.4, Standard Deviation = 1.4
- Mean = 3.0, Standard Deviation = 1.6
View Solution
14.
A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?
- \( 2 \)
- \( 3 \)
- \( 4 \)
- \( 5 \)
View Solution
15.
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:
- \( \frac{7}{5} \left( \frac{9}{10} \right)^4 \)
- \( \frac{7}{5} \left( \frac{9}{10} \right)^5 \)
- \( \frac{6}{5} \left( \frac{9}{10} \right)^4 \)
- \( \frac{6}{5} \left( \frac{9}{10} \right)^5 \)
View Solution

X	0	1	2	3	4	5	6	7
P(X)	1/12	1/12	1/12	1/12	1/12	1/12	1/12	1/12

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MHT CET PYQs for Probability with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Probability with Solutions

1.
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?

2.
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?

3.
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

4.
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.

5.
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?

6.
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.

7.
A die is rolled once. What is the probability of rolling a number greater than 4?

8.
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

9.
If two dice are rolled, what is the probability of getting a sum of 7?

10.
The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:

11.
If a random variable X has the following probability distribution values:
X 0 1 2 3 4 5 6 7
P(X) 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
Then P(X ≥ 6) has the value:

12.
A die is rolled. What is the probability of getting a number less than or equal to 4?

13.
Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:
Find the mean and standard deviation.

14.
A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

15.
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:

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MHT CET PYQs for Probability with Solutions

1.A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?

2.In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?

3.If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

4.In the word "UNIVERSITY", find the probability that the two "I"s do not come together.

5.A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?

6.A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.

7.A die is rolled once. What is the probability of rolling a number greater than 4?

8.The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \): \[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

9.If two dice are rolled, what is the probability of getting a sum of 7?

10. The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:

11.If a random variable X has the following probability distribution values:X01234567P(X)1/121/121/121/121/121/121/121/12Then P(X ≥ 6) has the value:

12.A die is rolled. What is the probability of getting a number less than or equal to 4?

13.Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution: Find the mean and standard deviation.

14.A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

15.A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:

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1.
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?

2.
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?

3.
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

4.
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.

5.
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?

6.
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.

7.
A die is rolled once. What is the probability of rolling a number greater than 4?

8.
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

9.
If two dice are rolled, what is the probability of getting a sum of 7?

10.
The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:

11.
If a random variable X has the following probability distribution values:
X 0 1 2 3 4 5 6 7
P(X) 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
Then P(X ≥ 6) has the value:

12.
A die is rolled. What is the probability of getting a number less than or equal to 4?

13.
Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:
Find the mean and standard deviation.

14.
A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

15.
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is: