Suppose that the reliability of a HIV test is specified as follows. Of people having HIV, 90% of the test detect the diséase but 10% go undetected. Of people free of HIV, 99% of the test judged HIV (-ve) but 1% are diagnosed as showing HIV (+ ve). From a large population of which 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist report him/her as HIV (+ve) What is the probability that the person actually has HIV?

Answer

0.083