The board of governors of Santa Clara University is contemplating mandatory testing of its student athletes. The test is

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The board of governors of Santa Clara University iscontemplating mandatory testing of its student athletes. The testis not 100% accurate. The conditional probabilities are as follows:If an athlete uses drugs, then the test will be positive 80% of thetime, whereas if he does not (i.e., he is a nonuser), the test willbe negative 70% of the time. Suppose the board suspects that 90% ofthe athletes do not use drugs.
a. Calculate the probability that if the test result ispositive, the athlete uses drugs, indeed. Show your work. (5points)
b. If a test costs $50, the cost of not identifying (andbarring) a drug user is $1,000, the cost of falsely accusing anon-user is $200, and other costs are zero, should the universitytest any athlete? Draw and use a decision tree. Show your work. (5points)