A problem by jinay patel

Suppose that the reliability of a HIV test is specified as follows: Of the people having HIV , 90 percent of the test detect the disease but 10 percent go undetected . Of people free of HIV , 99 percent of the test are judged HIV negative but 1 percent are diagnosed as showing HIV positive . From a large population of which only 0.1 percent have HIV , one person is selected at random , given the HIV test , and the pathologists reports him/her as HIV positive .What is the probability that the person actually has HIV. Let your answer comes to be x , then find the value of the following expression - x (1089)