Question

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

• A. $\frac{1}{729}$
• B. $\frac{8}{9}$
• C. $\frac{8}{729}$
• D. $\frac{8}{243}$

Answer 1

Answer: (D)

$\frac{8}{243}$

Probability of getting score $9$ in a single throw
$=\frac{4}{36}=\frac{1}{9}$
Probability of getting score $9$ exactly twice
${=}^3{C}_2\times {\left(\frac{1}{9}\right)}^2\times \frac{8}{9}=\frac{8}{243}$