[ExI] logic puzzle

[spike at rainier66.com]

I'm doing a test.  I get a different answer from the one the test publisher
offers.  Anyone want to take a crack at it?

 

 

 

The Annapolis Apples and the Boston Bananas play a series.  First team to
win 3 games wins the series.  Each team is equally likely to win each game,
no ties, games independent.

 

If the Bananas won the second game but the Apples won the series, what is
the probability that the Bananas won the first game?

 

 

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