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2002%20fall

# 2002%20fall - Fall 2002 Math 218 Final Examination J...

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Fall 2002 Math 218 Final Examination J. Cvitanic, L. Goldstein, L. Goukasian, C. Haskell, I. Kukavica, S. Lototsky, R. Mikulevicius, E. Verona, and Z. Vorel Problem 1 . In a large population, 1% of individuals are infected with a certain virus, say V . A test is applied to the whole population, and it is assumed that 99% of infected individuals test positive while 2% of noninfected individuals test positive. Let A be the event that a randomly chosen individual is infected with the virus V , and let B be the event that a randomly chosen individual tests positive for V . a) Construct a probability tree diagram describing this situation. b) Are events A and B independent? (Show your work.) c) For events A and B in the previous problem, find P ( A | B ) and P ( A | B ). d) Two randomly chosen individuals that are not infected with V are going to take this test. Find the probability that both of them will test positive for V . Problem 2 . A box contains 5 quarters, 4 dimes, and 2 nickels. a) We select 8 coins randomly without replacement. Find the probability that 4 or more of the selected coins are quarters. b) A coin is drawn randomly 5 times with replacement. Find the probability that we get at least one quarter. c) A coin is drawn 100 times with replacement. Find the probability that a quarter appears 50 or more times. Problem 3 . Customer arrivals to the Last-Minute-Holiday-Shopping-Store follow a Poisson distribution with the rate of 2 per hour.

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2002%20fall - Fall 2002 Math 218 Final Examination J...

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