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A ALEKS: Denise Hooper x ? -) C ? Secure? https://www-awhaleks.com/alekscg/x/bl.ew/loju.IgNslkgLjY22rR16. 2MaCShSKNukulhK4-ZbliWMO ALEKS INBOX REPORT OPTIONS Calculator Gradebook Calendar Review A certain disease occurs in 6% of the population. A test for the disease is fairly accurate: it misdassifies people with the disease as healthy 2% of the time and reports that a healthy person is diseased just 8% of the time. Suppose that a person tests positive for the disease. Compute the probability that the person does indeed have the disease. Round your answer to two decimal places. (If necessary, consult a list of formulas.) Clear Undo Help Next > Explain

Explanation / Answer

Here, we are given that:

P( disease ) = 0.06

P( negative test | disease ) = 0.02

P( positive test | no disease ) = 0.08

Using law of total probability, we get:

P( positive test ) = P( positive test | no disease )P( no disease ) + P( positive test | disease )P( disease )

P( positive test ) = 0.08*(1 - 0.06) + (1 - 0.02)*0.06 = 0.1340

Using Bayes theorem, we get here:

P( disease | positive test ) = P( positive test | disease )P( disease ) / P( positive test )

P( disease | positive test ) = (1 - 0.02)*0.06 / 0.1340 = 0.4388

Therefore 0.4388 is the required probability here.

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