Probability — Important Questions

0.7, 0, 1

Probability must be between 0 and 1 (inclusive). So 0.7, 0, and 1 are valid. 1.5 is greater than 1, and -0.2 is negative, so both are invalid.

2/5

Sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, so n(S) = 10. Prime numbers from 1 to 10 are {2, 3, 5, 7}, so n(A) = 4. Therefore, P(prime) = 4/10 = 2/5.

1/8

For three coins, n(S) = 8. Sample space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. All tails = {TTT}, so n(A) = 1. Therefore, P(all tails) = 1/8.

1/3

Sample space S = {1, 2, 3, 4, 5, 6}, so n(S) = 6. Numbers greater than 4 are {5, 6}, so n(A) = 2. Therefore, P(>4) = 2/6 = 1/3.