Blood donors are usually screened for HIV, both for the safety of the blood supply and for the benefit of the donor. The test, called an ELISA, tests positive 97.5% of the time if the donor actually has HIV. If the donor does not have HIV, the ELISA test correctly indicates that the person does not have the disease 92.6% of the time. About 0.2% of college students have HIV. After a blood drive at a college, the lab calls and tells a student that the test has indicated he has HIV. A. Use what you have learned in this lesson to determine the probability that the student actually has HIV. Because the prevalence of HIV is so small, it may be better to use 100,000 as your total population.
B. Considering the answers to questions 1 and 2, should you be more concerned about a positive test for a rare disease or a common disease? Explain your answer.