A pair of fair dice is thrown independently three times.

Question

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

Accepted Answer

Probability of getting score 9 in a single throw

$$ = {4 \over {36}} = {1 \over 9}.$$

Probability of getting score 9 exactly twice

$$ = {}^3{C_2} \times {\left( {{1 \over 9}} \right)^2} \times {8 \over 9} = {8 \over {243}}.$$

Solutions · 1