Heads given the ends differ

A fair coin is flipped 55 times. Given that the first and last flips came out opposite (one heads, one tails), what is the expected number of heads among all 55 flips?

Show hints (2)+
  1. Opposite ends contribute exactly 11 head, guaranteed.
  2. The middle three flips are unaffected by the condition: expected 1.51.5 heads. Add.

Answer

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2.5

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Asked at: Jane Street, Akuna Capital

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