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Math425Final

# Math425Final - Math 425(Fall 07 Final Exam 1 A committee of...

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Math 425 (Fall ’07) Final Exam December 17, 2007 1. A committee of size three is to be selected from a group of 6 Democrats, 5 Independents, and 4 Republicans. What is the probability that the Democrats have a majority on the committee? What is the conditional probability that the Democrats have a majority, given that at least one Republican is on the committee?

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2. We have a box containing four coins. The probability of getting head for the i -th coin is p = i 4 . One of the coin is drawn from the box and a head is flipped. What is the probability that the i -th coin was the coin chosen? 2
3. The time T (in hours) required to repair a machine is an exponential random variable with parameter λ = 3. The repair company charges the amount X for the repair (in dollars) determined by the formula X = 10 + e T 3 . What is the expected cost of the repair? 3

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4. We say that a multiple-choice test is well designed if the chance of passing the test by choosing randomly the answers is less than 5%. Suppose that we have a test for which there are 100
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Math425Final - Math 425(Fall 07 Final Exam 1 A committee of...

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