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 ±ight with Windy Airlines today, and I’ll ±y the same ±ight 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 ±ies 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 ±y 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. (c)
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05spex1 - Math 431 First Evening Exam Room B239, 6:00pm -...

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