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05spex1 - Math 431 First Evening Exam Room B239 6:00pm...

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Math 431 First Evening Exam Room B239, 6:00pm - 7:00pm, February 18, 2005 M´arton Bal´azs NAME: 1. My friend Bob takes the Madison - Nowheretown flight with Windy Airlines today, and I’ll fly the same flight tomorrow. This airline has three types, A , B and C , of planes, with 3, 4, and 6 seats per row, respectively. We know that the same plane flies to Nowheretown every day, but we don’t know of which type this plane is, so we estimate it could be each of the three types A , B or C with equal chance. We also know that seats are assigned completely randomly to passengers. (a) (15 points) What is the probability that I will have a window seat tomorrow? Answer: 2 3 · 1 3 + 2 4 · 1 3 + 2 6 · 1 3 = 1 2 . (b) (15 points) Later Bob tells me that he had a window seat. Then what is the probability that plane type A , B , or C , respectively, is the one to fly to Nowheretown? Answer: 2 3 · 1 3 1 2 = 4 9 , 2 4 · 1 3 1 2 = 1 3 and 2 6 · 1 3 1 2 = 2 9 , respectively.

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05spex1 - Math 431 First Evening Exam Room B239 6:00pm...

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