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HMMT 2001 U17

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Frank and Joe are playing ping pong. For each game, there is a 30%30 \% chance that Frank wins and a 70%70 \% chance Joe wins. During a match, they play games until someone wins a total of 21 games. What is the expected value of number of games played per match?

Dataset text NuminaMath olympiads. Quoted with source.

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30

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