7. During homecoming weekend, there are 3 big events: a football game, a basketb

Question

7. During homecoming weekend, there are 3 big events: a football game, a basketball game, and a movie in the stadium. The probability you go to the football game is 80%, the probability you go to the basketball game is 60%, and the probability you go to see the movie is 40%. Assume your attendance at an event is independent from your attendance at another event.

(a) Find the probability you go to the football game and the movie but not the basketball game.

(b) Find the probability that you go to the basketball game given that you go to only one event.

(c) Find the probability that you go to only the movie, given that you go to at least one event.

Explanation / Answer

a) P(Footboll and Move but not basketball) = 0.80*0.40*0.40 = 0.1280

b) P(Basketball /Only one event)

P(only one event) = 0.80*0.40*0.60+0.20*0.60*0.60+0.20*0.40*0.40 = 0.296

P(Basketball /Only one event) = (0.60*0.20*0.60)/0.296 = 0.243

c) P(At least one event) = 1-0.20*0.40*0.60 = 0.952

P(Only movie/At least one event) = 0.40/0.952 = 0.4202

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