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Probability - Gravner-38

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Assume $10$ % of people have a certain disease. A test gives the correct diagnosis with probability of $0.8$; that is, if the person is sick, the test will be positive with probability $0.8$, but if the person is not sick, the test will be positive with probability $0.2$. A random person from the population has tested positive for the disease. What is the probability that he is actually sick?(No, it is not $0.8$!)
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