A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$…
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is
$1 / 729$
$8 / 9$
$8 / 729$
$8 / 243$
Solution
Probability of getting score $9$ in a single throw $=\frac{4}{36}=\frac{1}{9}$
Probability of getting score $9$ exactly twice $={ }^3 \mathrm{C}_2 \times\left(\frac{1}{9}\right)^2 \times \frac{8}{9}=\frac{8}{243}$.