1.2.5 Two players, A and B, take turns on a gambling machine until one of them scores...

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1.2.5 Two players, A and B, take turns on a gambling machine until one of them scores a success, the first to do so being the winner. Their probabilities for success on a single play are p for A and q for B, and successive plays are independent.

(a) Determine the probability that A wins the contest given that A plays first.

(b) Determine the mean number of plays required, given that A wins.

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