Probability is one of the most important chapters in Class 10 Maths. It plays a crucial role in board exams and helps students understand real-life uncertainty and chance. In this post, we have provided important questions, MCQs, and case study-based problems based on the latest CBSE 2026 pattern to help you score high marks.

Class 10 Maths Probability – Important Questions

1. If two different dice are rolled together, the probability of getting an even number on both dice is:
(a) 1/36 (b) 1/2 (c) 1/6 (d) 1/4

2. In a family of 3 children, the probability of having at least one boy is:
(a) 7/8 (b) 1/8 (c) 5/8 (d) 3/4

3. The probability that a non-leap year selected at random will contain 53 Sundays is:
(a) 1/7 (b) 2/7 (c) 3/7 (d) 5/7

4. The probability of passing a certain test is $x/24$. If the probability of not passing is 7/8, then x is:
(a) 2 (b) 3 (c) 4 (d) 6

5. Two coins are tossed simultaneously. The probability of getting no head is:
(a) 1/4 (b) 1/2 (c) 3/4 (d) 1

6. A girl calculates that the probability of her winning a prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40 (b) 240 (c) 480 (d) 750

7. The probability of getting a number less than 5 in a single throw of a die is:
(a) 1/3 (b) 2/3 (c) 0 (d) 1/6

8. Two coins are tossed simultaneously. The probability of getting at least one head is:
(a) 1/4 (b) 1/2 (c) 3/4 (d) 1

9. In a survey, every fifth person has a vehicle. The probability that a person does NOT have a vehicle is:
(a) 1/5 (b) 5% (c) 4/5 (d) 95%

10. Two dice are thrown together. The probability of getting the difference of numbers equal to 3 is:
(a) 1/9 (b) 2/9 (c) 1/6 (d) 12/13

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11. 2 cards of heart and 4 cards of spade are missing from a pack of 52 cards. What is the probability of getting a black card?

12. A book consists of 100 pages. A page is opened at random. Find the probability that the page has a doublet number.

13. Find the probability that a number selected from 1 to 25 is not a prime number.

14. Lakshmi tosses two coins. Find the probability that she gets at most one head.

15. Find the probability that a leap year selected at random will contain 52 Sundays.

16. A bag contains 3 red, 5 black, and 7 white balls. Find probability that the ball drawn is:
(i) white (ii) red (iii) not black (iv) red or white

17. A number x is chosen from {-3, -2, -1, 0, 1, 2, 3}. Find the probability that $x^2 < 4$.

18. Two dice are thrown. Find probability of:
(i) even sum
(ii) sum ≥ 10
(iii) doublet of even numbers
(iv) multiple of 3
(v) prime sum

19. Three coins are tossed. Find probability of:
(i) all heads
(ii) no heads
(iii) at least two heads
(iv) at most one tail

20. Red queens and black jacks are removed from a deck. Find probability of:
(i) a king
(ii) red card
(iii) face card
(iv) queen

21. A die is rolled twice. Find probability that:
(i) 5 does not appear
(ii) 5 appears exactly once

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22. A card is drawn from a deck. Find probability that it is:
(i) a spade or an ace
(ii) a red king
(iii) neither king nor queen
(iv) either king or queen

23. A bag contains 5 red balls and some blue balls. Probability of blue is double of red. Find number of blue balls.

24. A box has balls numbered 1 to 20. Find probability that number is:
(i) prime
(ii) not divisible by 10
(iii) divisible by 2 or 3
(iv) divisible by 2 and 4

25. Cards numbered 2 to 101 are placed in a box. Find probability of selecting a perfect square number.

26. Two dice rolled. Find probability of even number on both dice.

27. Cards numbered 3, 5, 7, …, 37. Find probability of prime number.

28. Tickets numbered 11 to 30. Find probability that number is:
(i) multiple of 7
(ii) >15 and multiple of 5

29. In a cricket match, Karan faces 50 balls. Hits: 10 fours, 5 sixes, rest singles. Find probability of:
(i) four
(ii) single
(iii) no run

30. Assertion–Reason
Assertion: Probability of bad egg = 0.035 in 400 eggs → bad eggs = 14
Reason: Complementary probability = 1 − p

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📊 Case Study Questions

Total schools = 1000

Computers	Schools
1–10	250
11–20	200
21–50	290
51–100	180
101+	80

i) Probability of school having more than 100 computers
ii) Probability of ≤ 50 computers
OR
Probability of ≤ 20 computers
iii) Probability of ≤ 10 computers

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✅ Answers

1. d
2. a
3. a
4. b
5. a
6. c
7. b
8. c
9. c
10. b
11. 23/46
12. 10/100 = 1/10
13. 16/25
14. 3/4
15. 1/7
16. (i) 7/15 (ii) 3/15 (iii) 10/15 (iv) 10/15
17. 5/7
18. (i) 1/2 (ii) 6/36 = 1/6 (iii) 1/9 (iv) 12/36 = 1/3 (v) 15/36 = 5/12
19. (i) 1/8 (ii) 1/8 (iii) 4/8 = 1/2 (iv) 4/8 = 1/2
20. (i) 4/44 (ii) 24/44 (iii) 10/44 (iv) 2/44
21. (i) 25/36 (ii) 10/36 = 5/18
22. (i) 16/52 (ii) 2/52 (iii) 44/52 (iv) 8/52
23. 10 blue balls
24. (i) 8/20 (ii) 18/20 (iii) 13/20 (iv) 5/20
25. 9/100
26. 1/4
27. 9/18 = 1/2
28. (i) 3/20 (ii) 3/20
29. (i) 10/50 (ii) 35/50 (iii) 0
30. Assertion: True, Reason: True

Case Study:
i) 80/1000 = 2/25
ii) 740/1000 = 37/50
OR 450/1000 = 9/20
iii) 250/1000 = 1/4

❓ FAQs

Q1. Is Probability important for Class 10 boards?
Yes, it is a high-weightage chapter and often includes case study questions.

Q2. How many questions come from Probability?
Usually 3–5 questions including MCQs and long answer.

Q3. What is the most important concept in Probability?
Understanding sample space, favorable outcomes, and complementary probability.

Q4. Are dice and cards questions important?
Yes, they are very common in board exams.

To score high in Class 10 Maths, it is important to practice multiple chapters together rather than studying Probability alone. You should also solve questions from important chapters like Polynomials, Linear Equations in Two Variables, and Number Systems, as these topics frequently appear in board exams.

Make sure to practice Class 10 level MCQs and case study questions regularly to improve your accuracy and speed. Solving a variety of problems from different chapters will help you understand concepts deeply and perform better in your CBSE board exams.