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

Explanation

A:person is having HIV

B:test shows HIV positive

P(B/A)=0.9

P(B/A`'`)=0.01

P(A)=0.001

p(A/B)=`(P(B/A)*P(A))/(P(B/A)*P(A)+P(B/A')P(A'))`

=`(0.9*0.001)/(0.9*0.001+0.01*0.99)`

=`90/1089`