15+ Important CAT Probability Questions and Answers PDF Download

Overview: Get ready to practice the important CAT probability questions with solutions. Boost your prep with CAT level probability questions to ace with high percentile!

Looking to master questions on probability for CAT? You're in the right place! This blog brings you 25 carefully selected questions on probability for CAT, designed to challenge and sharpen your skills. These are CAT level probability questions that reflect the latest exam trends and difficulty.  

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Continue reading to get the list of CAT probability questions now!

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What are CAT Probability Questions?

Probability questions in the CAT are designed to test how well you can calculate the chances of events, such as drawing a card, tossing a coin, or selecting an item from a group. These problems measure both your logical reasoning and your ability to apply numerical concepts effectively.

To help you strengthen this area, we have provided 25+ CAT level probability questions for practice. Work through them, test your understanding, and then cross‑check your answers to see where you stand. 

15+ Important CAT Probability Questions to Practice Now!

1. A bag contains 3 red, 4 green and 5 blue balls. If two balls are drawn at random, what is the probability that they are both of the same color?

A) 2/11

B) 19/66

C) 1/11

D) 7/66

Correct Answer: B) 19/66

2. Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is 7?

A) 1/6

B) 1/36

C) 5/36

D) 1/12

Correct Answer: A) 1/6

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3. A box contains 10 electric bulbs, out of which 2 are defective. If 3 bulbs are chosen at random from the box, what is the probability that at least one of them is defective?

A) 7/15

B) 8/15

C) 7/12

D) 1/5

Correct Answer: B) 8/15 

4. A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a King or a Spade?

A) 4/13

B) 1/13

C) 16/52

D) 17/52

Correct Answer: C) 16/52

5. A coin is tossed 3 times. What is the probability of getting at least 2 heads?

A) 1/8

B) 3/8

C) 1/4

 D) 1/2

Correct Answer: D) 1/2 

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Easy Level CAT Probability Questions 2026

6. What is the probability that a leap year selected at random will contain 53 Sundays?

A) 2/7

B) 1/7

C) 3/7

D) 53/366

Correct Answer: A) 2/7

7. "A" Speak truth in 75% cases and B in 80% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

A) 5%

B) 15%

C) 60%

 D) 35%

Correct Answer: D) 35% 

8. A box contains 5 red and 4 blue balls. Two balls are drawn successively without replacement. What is the probability that the first ball is red and the second is blue?

 A) 5/18

B) 5/9

C) 4/9

D) 20/81

Correct Answer: A) 5/18

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9. In a class, 40% of the students study Math and 30% study Science. If 10% study both, what percentage of students study neither Math nor Science?

A) 40%

B) 20%

C) 60%

D) 30%

Correct Answer: A) 40%

10. Three unbiased coins are tossed. What is the probability of getting at most one tail?

A) 1/8

B) 3/8

C) 1/2

D) 7/8

Correct Answer: C) 1/2

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Moderate Level CAT Probability Questions 2026

11. A bag contains 6 white and 4 black balls. Two balls are drawn at random. What is the probability that they are of different colours?

A) 2/15

B) 7/15

C) 4/5

D) 8/15

Correct Answer: D) 8/15

12. From a group of 5 men and 3 women, 3 persons are selected at random. Find the probability that the selected group has 1 man and 2 women.

A) 15/56

B) 3/8

C) 5/8

D) 3/56

Correct Answer: A) 15/56

13. The probability that a student passes a Math test is 0.7 and an English test is 0.6. If the probability of passing at least one test is 0.85, what is the probability that the student passes both tests?

A) 0.45

B) 0.40

C) 0.55

D) 0.35

Correct Answer: A) 0.45

14. A single letter is chosen at random from the word "PROBABILITY". What is the probability that it is a vowel?

A) 3/11

B) 4/11

C) 4/11

D) 5/11

Correct Answer: C) 4/11

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Difficult Level CAT Probability Questions 2026

15. Two events A and B are such that P(A) = 0.4, P(B) = 0.3 and P(A and B) = 0.2. What is P(A or B)?

A) 0.9

B) 0.5

C) 0.7

D) 0.5

Correct Answer: D) 0.5

16. A family has two children. What is the probability that both children are girls, given that at least one of them is a girl?

A) 1/2

B) 1/3

C) 1/4

D) 2/3

Correct Answer: B) 1/3

17. A bag contains 5 red and 5 blue balls. If two balls are drawn at random with replacement, what is the probability that both are red?

A) 1/4

B) 1/2

C) 5/18

D) 1/9

Correct Answer: A) 1/4

18. If the probability of an event happening is p, what is the probability that it happens exactly 3 times in 5 trials (assuming independent trials)?

A) 5p^3(1-p)^2

B) 10p^3(1-p)^2

C) 10p^3(1-p)^2

D) 5C3 (p(1-p))^3

Correct Answer: B) 10p^3(1-p)^2

19. A committee of 4 persons is to be chosen from 6 men and 4 women. What is the probability that there are exactly 2 men and 2 women in the committee?

A) 3/7

B) 3/8

C) 1/2

D) 5/14

Correct Answer: A) 3/7

20. What is the probability that the sum of two numbers chosen from the set {1, 2, 3, ..., 10} is odd, if the numbers are chosen without replacement?

A) 5/9

B) 1/2

C) 4/9

D) 1/5

Correct Answer: A) 5/9

Important Probability Formulas (Table Format)

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Important Probability Formulas for CAT 2026

For practising CAT Probability Questions, aspirants need to be familiar with the key probability formulas. Here is the list of some of the essential probability formulas for CAT 2026:

Concept/Rule	Description	Formula
Basic Probability	The likelihood of an event A occurring.	P(A) = n(A) / n(S) n(A) = Number of Favorable Outcomes, n(S) = Total Outcomes in Sample Space
Probability Range	The value range for any probability.	0 ≤ P(A) ≤ 1
Rule of Addition (Union of Events)	Probability of event A OR event B (or both) occurring.	P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Rule of Complementary Events	Probability of an event A NOT occurring (A').	P(A') = 1 - P(A) Also, P(A) + P(A') = 1
Disjoint / Mutually Exclusive Events	Events A and B cannot occur at the same time.	P(A ∩ B) = 0 If disjoint, P(A ∪ B) = P(A) + P(B)
Independent Events	The occurrence of one event does not affect the occurrence of the other.	P(A ∩ B) = P(A) · P(B)
Conditional Probability	Probability of event A occurring GIVEN that event B has already occurred.	P(A | B) = P(A ∩ B) / P(B) Provided P(B) ≠ 0
Bayes' Formula	Updates the probability of an event based on new evidence.	P(A | B) = (P(B | A) · P(A)) / P(B)

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Conclusion

Lastly, having a good grasp of CAT probability questions and CAT probability formulas is a significant advantage in achieving a good percentile in the main exam.

Practicing the CAT level probability questions not only helps you to understand the type of CAT probability combinatorics questions asked in the exam, but it also makes you aware of the difficulty level.

By practicing these core concepts and recognizing common problem types, you can confidently tackle CAT probability combinatorics questions and boost your score in the CAT exam.