Question

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is 

(A) 1/729 

(B) 8/9 

(C) 8/729

(D) 8/243

Answer 1

Answer is (D) 8/243

Probability of getting score 9 in a single throw is,

4/36 = 1/9

Probability of not getting score 9 in a single throw is,

1 - 1/9 = 8/9

Therefore, probability of getting score 9 exactly twice is

³C₂ x (1/9)² x (8/9)^{3 - 2} = 8/243