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A coin is tossed repeatedly; on each toss a head is shown with probability p, satisfying 0 < p < 1, and a tail with probability 1 - p. All tosses are mutually independent. Let E denote the event that two successive heads occur earlier than two successive tails. With A denoting the outcome of the first toss, argue that P(E | A = head) = p + (1 - p) P(E | A = tail). Find a similar expression for P(E | A = tail), and then solve the two equations and compute P(E).

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