A diagnostic test is used by a clinic to determine whether or not a person has a

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A diagnostic test is used by a clinic to determine whether or not a person has a certain disease. If the test is positive (T) the person is assumed to have the disease, while if the test is negative (T^c) the person is assumed not to have the disease. Let E₁ be the event that a person has the disease. Suppose P(E₁) = 0.3, P(T|E₁) = 0.9, and P(T^c|E₂) = 0.8 where E₂is "not E₁".

1. Find the probability that the test is positive.

2. A mistaken diagnosis occurs when either (i) the test is negative and the person has the disease or (ii) the test is positive and the person does not have the disease. What is the probability that the clinic will make a mistaken diagnosis?

3. Find the probabilities P(E₁|T), P(E₁|T^c), P(E₂|T), and P(E₂|T^c).

Posted Date: May 18, 2024 11:17 PM

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