olymmath

HMMT November 2009 U11

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Lily and Sarah are playing a game. They each choose a real number at random between -1 and 1 . They then add the squares of their numbers together. If the result is greater than or equal to 1 , Lily wins, and if the result is less than 1, Sarah wins. What is the probability that Sarah wins?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\pi}{4}

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