Probability | Part IA, 2008

AA and BB play a series of games. The games are independent, and each is won by AA with probability pp and by BB with probability 1p1-p. The players stop when the number of wins by one player is three greater than the number of wins by the other player. The player with the greater number of wins is then declared overall winner.

(i) Find the probability that exactly 5 games are played.

(ii) Find the probability that AA is the overall winner.

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