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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

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.

Determine the probability that A wins the contest given that A plays first.

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