An athletic league does drug testing of its athletes, 10 percent of whom use drugs. This test, however, is only 95 percent reliable. That is, a drug user will test positive with probability 0.95 and negative with probability 0.05, and a nonuser will test negative with probability 0.95 and positive with probability 0.05.

Develop a probability tree diagram to determine the posterior probability of each of the following outcomes of testing an athlete.

(a) The athlete is a drug user, given that the test is positive.

(b) The athlete is not a drug user, given that the test is positive.

(c) The athlete is a drug user, given that the test is negative.

(d) The athlete is not a drug user, given that the test is negative.

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(e) Use the corresponding Excel template to check your answers in the preceding parts.