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Suppose that the reliability of a test for the detection of a disease such as AIDS...

Suppose that the reliability of a test for the detection of a disease such as AIDS is as follows: Of those having AIDS, 90 % were detected by the test but 10 % go undetected. Further among those free of AIDS, 99 % are detected free of the disease by the test but 1 % are diagnosed as having AIDS by the test. Suppose the probability for a person to contact AIDS is 0.001. If a person chosen at random is diagnosed as having AIDS by the test, analyze and compute the probability that the person is in fact contracted with the AIDS.

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