Testing for AIDS, I The ELISA test can help detect whether people have the AIDS virus (HIV). As with any medical test, ELISA can give false positive and false negative results. From experience, medical researchers estimate that the ELISA test has a 0.2% false positive rate and a 0.1% false negative rate. Suppose we use the ELISA test in an area where 5% of the population has HIV.

(a) Draw a tree diagram that models this situation.

(b) Find the probability that a randomly selected person from this area would test positive. Show your work.

(c) Given that a randomly chosen person has tested positive, what’s the probability that the person actually has HIV? Show your work.