Problem 8 (20 pts). A drug-screening test is used in a large population of people of whom 5% actually use drugs. Suppose that the false positive rate is 9% and the false negative rate is 3%. Let D a randomly selected person uses the drug D a randomly selected person does not use the drug TP a randomly selected person tests positive TN a randomly selected person tests negative Calculaye the following probabilities. (a) P(D). (b) P(D). (c) P(TP | D). (d) P(TN | D). (e) P(TN | D). (f) P(TP | D). Hint: One has PE F) 1-P(E | F) Problem 9 With the assumptions of problem 8 answer the following questions. (a) A randomly selected person tests positive. What is the probability that he uses the drug? (b) A randomly selected person tests negative. What is the probability that he does not use the drug? Hint: Use Bayes' formula P(FE)P(E) P(E F): P(FE)P(E)+P(F | E)P(E)