In a game between two equal teams, the home team wins with probability p > 1 / 2. 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 P [ H ] , the probability that the team with the home advantage wins the series

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LaToyaShante73531idn LaToyaShante73531idn

07-03-2022
Mathematics

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In a game between two equal teams, the home team wins with probability p > 1 / 2. 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 P [ H ] , the probability that the team with the home advantage wins the series

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Topeadeniran2idn Topeadeniran2idn · Answer 1 · 2022-03-18T14:00:33-04:00

The probability that the team with the home advantage wins the series is 2P - 3P² + 2P³.

How to calculate the probability?

From the information given, the home team wins with probability p > 1/2.

Therefore, losing a game at home is given has probability 1-P. Similarly, winning the home team in a game at away probability will be 1-P.

Therefore, the probability that the team with the home advantage wins the series will be:

P(T) = P(1 - P) + (P × P × P) + (1 - P)(1 - P)(P)

= P - P² + P³ + (P - 2P² + P³)

= 2P - 3P² + 2P³

In conclusion, the probability is 2P - 3P² + 2P³.

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