What is the probability that Team (B) wins the series given that Team (B) wins the first

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What is the probability that Team \(B\) wins the series given that Team \(B\) wins the first game?

We consider two baseball teams playing a best-of-three series (meaning the first team to win two games wins the series). Team A is a little bit better than Team B, so we expect Team A will win \(55 \%\) of the time.

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