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#042 · conditional_probabilitydifficulty 3

A fair coin is flipped until the first head. What is the expected number of flips?

alt explanation → Think of it recursively. Let E be the expectation. With probability ½ we finish in 1 flip; with probability ½ we've wasted a flip and are back where we started, so E = ½·1 + ½·(1+E). Solve: E = 2.

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