Suppose that a new Internet company Mumble .com requires all employees to take a drug test. Mumble .com can afford only the inexpensive drug test—the one with a 5% false-positive rate and a 10% false-negative rate. (That means that 5% of those who are not using drugs will incorrectly test positive and that 10% of those who are actually using drugs will test negative.) Suppose that 10% of those who work for Mumble.com are using the drugs for which Mumble is checking. It may be helpful to draw a tree diagram to answer the questions that follow.

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

b. If one employee is chosen at random, what is the probability that the employee does not use drugs but tests positive anyway?

c. If one employee is chosen at random, what is the probability that the employee tests positive?

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