Two players A and B play a game of dice . They roll a pair of...

Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ?

Expert Solution

Total sample space = 6 * 6 = 36

Sample space for rolling a 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

P(rolling a 7) = 6 / 36 = 1/6

Let A represents that A rolls a 7 and A' represent A does not roll a 7.

P(B winning the game) = P(A' B) + P(A' B' A' B) + P(A' B' A' B' A' B) + ...

= [(5/6) * (1/6)] + [(5/6)³ * (1/6)] + [(5/6)⁵ * (1/6)] + ...

= (5/6) * (1/6) / (1 - (5/6)²)

= 5/11 or 0.4545

orchestra answered 2 years ago

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