Question

Three brothers Alex(A), Nick(N) and Danny (D) play a game where they roll a die, they...

Three brothers Alex(A), Nick(N) and Danny (D) play a game where they roll a die, they do this in the order ANDAND .... What is the probability that, of the three players, A is the first to throw a 6, N the second, and D is the third?

Math   Statistics-And-Probability   
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Answer #1

P(getting a 6) = 1/6

P(not getting a 6) = 1 - 1/6 = 5/6

Probability = P(getting a 6) * P(getting a 6) * P(getting a 6) + P(not getting a 6) * P(not getting a 6) * P(not getting a 6) * P(getting a 6) * P(getting a 6) * P(getting a 6) + P(not getting a 6) * P(not getting a 6) * P(not getting a 6) * P(not getting a 6) * P(not getting a 6) * P(not getting a 6) * P(getting a 6) * P(getting a 6) * P(getting a 6) + ...

                = (1/6)3 + (5/6)3 (1/6)3 + (5/6)6 (1/6)3 + ...

                = (1/6)3 / (1 - (5/6)3)

                = 1/91 (ans)

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