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Previous Year Question (PYQs)

A pair of fair dice is thrown independently 3 times. The probability of getting a score of exactly 9 twice is




Solution

$P(\text{sum} = 9) = \dfrac{4}{36} = \dfrac{1}{9}$ $\Rightarrow P(\text{exactly 2 times}) = \binom{3}{2}\left(\dfrac{1}{9}\right)^2\left(\dfrac{8}{9}\right) = 3 \times \dfrac{1}{81} \times \dfrac{8}{9} = \dfrac{8}{243}$

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