Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Possibilities of getting 9 are (5, 4), (4, 5), (6, 3), (3 6)
$\therefore p=\frac{4}{36}=\frac{1}{9}andq=1-p=1-\frac{1}{9}=\frac{8}{9}$
Therefore, the required probability is
${}^3{C}_2{q}^1{p}^2=\left(3\right)\left(\frac{8}{9}\right){\left(\frac{1}{9}\right)}^2=\frac{8}{243}$