olymmath

HMMT November 2010 F6

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When flipped, a coin has a probability pp of landing heads. When flipped twice, it is twice as likely to land on the same side both times as it is to land on each side once. What is the larger possible value of pp ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3+\sqrt{3}}{6}

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