A new HIV test identifies 95% of people who are really HIV positive and 98% of people who are really HIV negative. Only 1 in a 1000 of the population are HIV positive. If the HIV test shows a positive...

Extracted text: A new HIV test identifies 95% of people who are really HIV positive and 98% of people who are really HIV negative. Only 1 in a 1000 of the population are HIV positive. If the HIV test shows a positive result, the individual might wish to retake the test. Suppose that the results of a person retaking the HIV test are conditionally independent given HIV status (clearly two results of the test would certainly not be unconditionally independent). Suppose a person takes the test, the test is positive, the person takes the test again and the test is again positive. What is the probability that the person actually has HIV?