Suppose that 10% of 7-year-olds in Madison, Wisconsin, like the Chicago Bears, 7

Question

Suppose that 10% of 7-year-olds in Madison, Wisconsin, like the Chicago Bears, 75% like the Green Bay Packers, and the remaining 15% like some other team. (These are professional football teams.) Suppose that the probability of a 7-year-old fan of the Chicago Bears going to a game in a given year is 0.01, the probability of a 7-year-old Green Bay Packers fan going to a game in a given year is 0.05, and the probability of a 7-year-old fan of a different team going to a game in a given year is 0.005. A 7 year old is selected randomly from Madison.

(a) What is the probability that the selected 7 year old goes to a professional football game next year?

(b) If the selected 7 year old does go to a game in the coming year, what is the probability that this 7 year old was a fan of the Packers?

Explanation / Answer

a) probability that the selected 7 year old goes to a professional football game next year=P(fan of Chicago Bears and goes to the game +fan of Green Bay Packers and goes to the game +fan of other team and goes to the game )

=0.10*0.01+0.75*0.05+0.15*0.005=0.03925

b)probability that this 7 year old was a fan of the Packers given goes to the game

=P(probability that this 7 year old was a fan of the Packers)/P( goes to the game)

=0.75*0.05/0.03925=0.9554

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