Expected flips for two heads (not in a row)

A fair coin is flipped until two heads in total have appeared - they do not need to be consecutive. What is the expected number of flips?

Show hints (2)+
  1. Progress is never lost: the wait splits into two separate waits for a single head.
  2. Each wait for a head with p=12p = \tfrac12 has mean 2.

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