Class 10 (SSC Board)Mathematics & Statistics2026-27 Syllabus
Chapter 5 Probability Practice Set 5.3 Solutions
Complete Maharashtra State Board Balbharati & Yuvakbharati textbook solutions for Chapter 5 Probability Practice Set 5.3. Step-by-step solved exercises, numerical problems, and digest answers.
1 Solved Questions• 1090 words
Practice Set 5.3 Algebra 10th Std Maths Part 1 Answers Chapter 5 Probability
Question 1Maharashtra Board Solution
Write sample space ‘S’ and number of sample points n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).
i. One die is rolled, Event A: Even number on the upper face. Event B: Odd number on the upper face. Event C: Prime number on the upper face.
ii. Two dice are rolled simultaneously, Event A: The sum of the digits on upper faces is a multiple of 6. Event B: The sum of the digits on the upper faces is minimum 10. Event C: The same digit on both the upper faces.
iii. Three coins are tossed simultaneously. Condition for event A: To get at least two heads. Condition for event B: To get no head. Condition for event C: To get head on the second coin.
iv. Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits. Condition for event A: The number formed is even. Condition for event B: The number is divisible by 3. Condition for event C: The number formed is greater than 50.
v. From three men and two women, environment committee of two persons is to be formed. Condition for event A: There must be at least one woman member. Condition for event B: One man, one woman committee to be formed. Condition for event C: There should not be a woman member.
vi. One coin and one die are thrown simultaneously. Condition for event A: To get head and an odd number. Condition for event B: To get a head or tail and an even number. Condition for event C: Number on the upper face is greater than 7 and tail on the coin.
Solution & Step-by-Step Answer:
i. Sample space (S) = {1, 2, 3, 4, 5, 6} ∴ n(S) = 6 Condition for event A: Even number on the upper face. ∴ A = {2,4,6} ∴ n(A) = 3 Condition for event B: Odd number on the upper face. ∴ B = {1, 3, 5} ∴ n(B) = 3 Condition for event C: Prime number on the upper face. ∴ C = {2, 3, 5} ∴ n(C) = 3
ii. Sample space, S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} ∴ n(S) = 36 Condition for event A: The sum of the digits on the upper faces is a multiple of 6. A = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)} ∴ n(A) = 6
Condition for event B: The sum of the digits on the upper faces is minimum 10. B = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} ∴ n(B) = 6
Condition for event C: The same digit on both the upper faces. C = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} ∴ n(C) = 6
iii. Sample space, S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} ∴ n(S) = 8
Condition for event A: To get at least two heads. ∴ A = {HHT, HTH, THH, HHH} ∴ n(A) = 4
Condition for event B: To get no head. ∴ B = {TTT} ∴ n(B) = 1
Condition for event C: To get head on the second coin. ∴ C = {HHH, HHT, THH, THT} ∴ n(C) = 4
iv. Sample space (S) = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54} ∴ n(S) = 25 Condition for event A: The number formed is even ∴ A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54) ∴ n(A) = 13 Condition for event B: The number formed is divisible by 3. ∴ B = {12, 15, 21, 24, 30, 42, 45, 51, 54} ∴ n(B) = 9 Condition for event C: The number formed is greater than 50. ∴ C = {51,52, 53,54} ∴ n(C) = 4
v. Let the three men be M1, M2, M3and the two women be W1, W2. Out of these men and women, a environment committee of two persons is to be formed. ∴ Sample space, S = {M1M2, M1M3, M1W1, M1W2, M2M3, M2W1, M2W2, M3W1, M3W2, W1W2} ∴ n(S) = 10 Condition for event A: There must be at least one woman member. ∴ A = {M1W1, M1W2, M2W1, M2W2, M3W1, M3W2, W1W2} ∴ n(A) = 7 Condition for event B: One man, one woman committee to be formed. ∴ B = {M1W1, M1W2, M2W1, M2W2, M3W2, M3W2} ∴ n(B) = 6 Condition for event C: There should not be a woman member. ∴ C = {M1M2, M1M3, M2M3} ∴ n(C) = 3
vi. Sample space, S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)} ∴ n(S) = 12 Condition for event A: To get head and an odd number. ∴ A = {(H, 1), (H, 3), (H, 5)} ∴ n(A) = 3 Condition for event B: To get a head or tail and an even number. ∴ B = {(H, 2), (H, 4), (H, 6), (T, 2), (T, 4), (T, 6)} ∴ n(B) = 6 Condition for event C: Number on the upper face is greater than 7 and tail on the coin. The greatest number on the upper face of a die is 6. ∴ Event C is an impossible event. ∴ C = { } ∴ n(C) = 0