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

AIEEEAIEEE 2007Probability - Part 2

Solution:

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