Question

Your favorite team is in the World Series. You have assigned a probability of 62% that they vwill win the World Series. Past records indicate that when teams win the World Series, they won the first game of the series 70% of the time. When they lose the World Series, they won the first game 23% of the time. The first game is over and your team has lost. What is the probability that they will win the World Series?

Answer 1

This is a Bayes Theorem question. First listing the given events, we have:

• Pr(Win the championship) = .62
• Pr(Win the first game | Win the championship) = .70
• Pr(Win the first game | Lose the championship) = .23

From these we also know/can derive:

• Pr(Lose the championship) = 1-.62 = .38
• Pr(Lose the first game | Win the championship) = 1-.70 = .30
• Pr(Lose the first game | Lose the championship) = 1-.23 = .77

And we want Pr(win the championship | Lose the first game) = ?

Using Bayes theorem, Pr(Win the championship | Lose the first game) = [Pr(Lose the first game | Win the championship) × Pr(Win the championship)] ÷ [Pr(Lose the first game | Win the championship) × Pr(Win the championship) + Pr(Lose the first game | Lose the championship) × Pr (Lose the championship)]

Therefore we have Pr (Win the championship | Lose the first game) = (.30)(.62) ÷ [(.30)(.62) + (.77)(.38)] = .3886335

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