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