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In order to get into a bowl game, UConn Football has to win at least 5...

In order to get into a bowl game, UConn Football has to win at least 5 of 9 games. Let’s assume that they are equally likely to win or to lose each game, independently of the other games. We have two fans who are also probability experts, but each with different information provided:

Fan A was at the first game, and witnessed UConn winning. Based on this information the probability UConn gets into a bowl game is PA.

Fan B was in a coma all season, and when woke up asked the doctor if she knew how the season ended. All the doctor could tell was that UConn had won at least one game in the regular season (she could not tell which). Fan B then calculates the probability that UConn got into a bowl game and finds it to be PB.

Which is larger, PA or PB?

Math   Statistics-And-Probability   
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