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To determine which of two people gets a prize, a coin is flipped twice. If the flips are a Head and then a Tail, the first player wins. If the flips are a Tail and then a Head, the second player wins. However, if both coins land the same way, the flips donâ€™t count and whole the process starts over.

Assume that on each flip, a Head comes up with (constant) probability p, regardless of what happened on other flips. Find the probability that the first player wins.