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HMMT 2007 F5

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A best of 9 series is to be played between two teams. That is, the first team to win 5 games is the winner. One of the teams, the Mathletes, has a 2/32 / 3 chance of winning any given game. What is the probability that the winner is determined in the 7th game?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{20}{81}

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