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You are about to play a series of 9 chess games online against an opponent called...

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You are about to play a series of 9 chess games online againstan opponent called EliteChampion. The first to win 5 games wins theseries. (Ignore the possibility of a draw.) You know thatEliteChampion is most likely your friend, Jenna. There’s a 20%chance EliteChampion is your Mom, and that’s the only otherpossibility. You beat your Mom 70% of the time, but you only beatJenna 40% of the time. Given that you won the first game, what isthe probability you will win the series? Give an exact answer andalso give a numerical approximation, correct to four decimalplaces.

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