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midterm108

# midterm108 - Math 425(Fall 08 Midterm 1 October 2 2008 1(10...

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Math 425 (Fall ’08) Midterm 1 October 2, 2008 1 (10 pts) A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from a group of 5 Republicans, 6 Democrats, and 4 Independents. How many committees are possible?

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2 (10 pts) A forest contains 20 elk, of which 7 are captured, tagged, and then released. A certain time later 5 of the 20 elk are captured. What is the probability that 2 of these 5 have been tagged? 2
3 (20 pts) Each of 2 balls is painted either black or gold and the place in an urn. Suppose that each ball is colored black with probability 1 2 , and that these events are independent. a) Suppose that you obtain information that the gold paint has been used (and thus at least one of the balls is painted gold). Compute the conditional probability that both balls are painted gold. b) Suppose, now, that the urn tips over and 1 ball falls out. It is painted gold. What is the conditional probability that both balls are gold in this case?

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midterm108 - Math 425(Fall 08 Midterm 1 October 2 2008 1(10...

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