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A coin having probability p of coming up heads is successively flipped until two of the...

A coin having probability p of coming up heads is successively flipped until two of the most recent three flips are heads. Let N denote the number of flips. (Note that if the first two flips are heads, then N = 2.) Find E[N]. (please do not just copy the answer from other solutions, I need a thoroughly explained answer)

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