Let HIV represent the event that a randomly selected American has the HIV virus, and let HIV' represent the event that a randomly selected American does not have this virus. Since it is estimated that .6 percent of the American population has the HIV virus, P(HIV) = .006 and (HIV') = .994. A diagnostic test is used to attempt to detect whether a person has HIV. According to historical data, 99.9 percent of people with HIV receive a positive (POS) result when this test is administered, while 1 percent of people who do not have HIV receive a positive result. That is, P(POS|HIV) = .999 and P(POS|HIV' ) = .01. If we administer the test to a randomly selected American (who may or may not have HIV) and the person receives a positive test result, what is the probability that the person actually has HIV?