1. A medical test for HIV infection has three possible test results: positive ( ), negative ( ),
and inconclusive ( ). Given that a person is infected, the probabilities of these outcomes
are: 0.85, 0.10, and 0.05, respectively. Given that a person is not infected, the probabilities
of these outcomes are: 0.02, 0.90, and 0.08. Assume that 2% of the general population are
infected with HIV. A random person from the population is tested. [Hint: let be the event
that this person is infected. So
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The solution gives detailed steps on calculating conditional probability using Bayes's formula in a specific decision making example. All formula and calculations are shown and explained.