Question

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

• A. $8/729$
• B. $8/243$
• C. $1/729$
• D. $8/9$

Answer 1

The correct option is B $8/243$

Possibility of getting 9 are $(5,4),(4,5),(6,3).(3,6)$
Probability of getting score 9 in a single throw $=P=\frac{4}{36}=\frac{1}{9}$
Required probability $=$ probability of getting score 9 exactly twice ${=}^3{C}_2{\left(\frac{1}{9}\right)}^2\times \left(\frac{8}{9}\right)=\frac{8}{243}$