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In the baseball World Series, two teams play games until one team has won four games;...

In the baseball World Series, two teams play games until one team has won four games; thus the total length of the series must be between 4 and 7 games. What is the probability of having a World Series with a length of 4 games under the assumption that the games are independent events with each team equally likely to win?

Math   Statistics-And-Probability   
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Answer #1

This question follows binomial distribution with number of possible outcomes is 2 and the probability of each outcome, whether winning or losing is 0.5. The probability of having a World Series with a length of 4 games is =

There are only two cases when this is possible. Either the team 1 win the first 4 matches or the team 2 wins the first 4 matches. The probability of both the events happening is the same.

Now the probability of team 1 winning the first 4 matches = 4C4 * (0.5)4 * (0.5)0

= 0.0625

The Probability of team 2 winning the first 4 matches will also be 0.0625

The required probability = 0.0625 + 0.0625 = 0.125

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