“Take you on at billiards,” said Cue to Ball. ” Right you are,” said Ball. “We’ll play five games.” “I ought to beat you, Ball , you know,” said Cue. “Of course,” said Ball. “You’ll have to give me odds.” “How do my chances of winning compare with yours?” asked Cue. ” Well,” replied Ball, “I’ll tell you. Your chance of winning three of the five games and your chance of winning four of the five games are, according to my calculations, exactly the same.”

What is the chance (according to Ball’s calculations) that Cue will win all five games? How could he determine his chances of sweeping the series given any set of calculations?

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