Duration: 10:10

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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 \( \mathrm{HIV} \), \( 99 \% \) 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 \( \mathrm{HIV} \), oneperson is selected at random, given the HIV test, and the pathologist reports him/her s \( \mathrm{HIV}+ \) ive. What is the probability that the person actually has HIV?
\( \mathrm{P} \)
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