Refer to the previous exercise. Suppose that because of the high rate of false-positives for the drug test, Mumble.com has instituted a mandatory independent second test for those who test positive on the first test.

a. If one employee is selected at random, what is the probability that the selected employee uses drugs and tests positive twice?

b. If one employee is selected at random, what is the probability that the employee tests positive twice?

c. If we know that the randomly chosen employee has tested positive twice, what is the probability that he or she uses drugs?

d. What is the chance that an individual who does use drugs doesn’t test positive twice (either this employee tests negative on the first round and doesn’t need a retest, or this employee tests positive the first time and that result is followed by a negative result on the retest)?

e. Discuss the benefits and drawbacks of using a retest scheme such as the one proposed in this question.