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Suppose a blood test for a certain kind of disease, call it “disease A”

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Suppose a blood test for a certain kind of disease, call it “disease A”, produces a positive test result (that the person has the disease) in 99% of cases where the person is known (by some other method) to have disease A; and it produces a negative test result (that the person does not have the disease) in 97% of cases where the person is known to not have disease A. In addition, suppose that 1% of the population has disease A. You go in for the blood test and your doctor says, “bad news, the test came back positive”. Should you be worried? Answer this question by calculating the (conditional) probability that you have disease A based on the knowledge of your positive blood test. Show your work.

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[Solved] Suppose a blood test for a certain kind of disease, call it “disease A”

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