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: (D)

$8/243$

Answer 2

Probability of getting score 9 in a single throw $=\frac{4}{36}=\frac{1}{9}$ Probability of getting score 9 exactly twice $=^{3}C_{2}\times\left(\frac{1}{9}\right)^{2}\times\frac{8}{9}=\frac{8}{243}.$