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