Consider a blood test for a disease. If the patient has the disease, test is positive with probability 0.97. If the patient does not have the disease, the test is negative with probability 0.92. 1 in 10,000 people have the disease. If a person tests positive, what is the probability he or she actually has the disease?

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Consider a blood test for a disease. If the patient has the disease, test is positive with probability 0.97. If the patient does not have the disease, the test is negative with probability 0.92.
1 in 10,000 people have the disease. If a person tests positive, what is the probability he or
she actually has the disease?

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