The annual Atlantic Coast Conference men\'s basketball tournament has temporaril

Question

The annual Atlantic Coast Conference men's basketball tournament has temporarily taken Joe's mind off the Chicago Cubs. He says to himself, "I think that Florida State has probability 0.1 winning. North Carolina's probability is twice Florida State's, and Duke s is three times Florida State's." (a) What are Joe's personal probabilities for North Carolina? What are Joe's personal probabilities for Duke? (b) What is Joe's personal probability that one of the 12 teams other than Florida State, North Carolina, and Duke win the tournament?

Explanation / Answer

a) Joe's personal probability for North Caroline = 2(Probability of Florida) = 2(0.1) = 0.2

Joe's personal probability for Duke = 3(Probability of Florida) = 3(0.1) = 0.3

b) Joe's personal probability that any team except these three will win

= 1 - P(One of these three will win)

= 1 - (0.1 + 0.2 + 0.3)

= 1 - 0.6

= 0.4

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