HIV Testing: In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of the tests were (correctly) positive, while for people without HIV, 98.5% of the tests were (correctly) negative. A clinic serving an at-risk population offers free HIV testing, believing that 15% of the patients may actually carry HIV. (Hint: a tree diagram may be helpful)
a) What is the probability that a person will test positive for HIV?
b) What is the probability that a person will test negative for HIV?
c) What is the probability that a person testing negative is truly free of HIV?