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A pair of fair dice is thrown independently three times.

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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

(a) 8/729 

(b) 8/243

(c) 1/729 

(d) 8/9.

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(b) : Possibility of getting 9 are (5, 4), (4, 5), (6, 3), (3, 6)
Probability of getting score 9 in a single throw = p  = 4/36  = 1/9
Required probability = probability of getting score 9 exactly twice = 3C2(1/9)2 x (8/9) = 8/243.

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