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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

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: if the first two flips are heads, then N=2.) Find E[N], ( expectation of N)

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