Probability - Home Field Advantage

In a game between two equal teams, the home team wins any game with probability P. In a best of three playoff series, a team with the home advantage has a game at home, followed by a game away, followed by a home game if necessary. The series is over as soon as one team wins two games. What is the probability that the team with home advantage wins the series ? Is the home advantage increased by playing a three-game series rather than one-game play-off ?

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