Fair price of a heads-majority bet

A fair coin is flipped four times. A bet pays $10 if heads are a strict majority (more heads than tails) and $0 otherwise. What is its fair price (in dollars, to two decimals)?

Show hints (2)+
  1. Four flips can tie 2–2, which is not a majority - so it is not simply 1/21/2.
  2. Count (43)+(44)=5\binom{4}{3}+\binom{4}{4}=5 winners out of 1616, then multiply by $10.

Answer

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3.13 (± 0.01)

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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