Who wins the first head?

Players A and B alternately toss a fair coin, with A going first. The first to flip heads wins. What is P(A wins)? (to 3 decimals)

Show hints (2)+
  1. Sum a geometric series over A's turns.
  2. Or set up a one-line recursion.

Answer

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0.6667 (± 0.005)

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Asked at: Optiver, IMC

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