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Problem 1. Joe is a randomly chosen member of a large population in which 3% are heroin users. Joe went for a test that correctly identifies users 95% of the time and correctly identifies nonusers 90% of the time. (a) Given that Joe is not a heroin user, find the probability that he tests positive. (b) Given that Joe tested positive, find the probability that he is a heroin user. (c) Given that Joe tested negative, find the probability that he is not a heroin user