HW A state health department reports a 15% rate of a certain virus for the at ri

Question

HW A state health department reports a 15% rate of a certain virus for the at risk population Under certain conditions, a preliminary screening test for the virus is correct 90% of the time (Subjects are not told that 02/2 they are infected until additional tests verify the results.) If someone is randomly selected from the at-risk population, what is the probability that they have the virus if it is known that they have tested positive in ed: 02/2 the initial screening? 55.1 3 pe (Round to three decimal places as needed) ore: The probability that the at-risk subject has the virus is Questions Cl on 1 (1/2)

Explanation / Answer

Solution:
Prob(infected | positive test) = [Prob(positive test | infected)Prob(infected)]/Prob(positive test)
= .90x.15/Prob(positive test)
But Prob(positive test) = Prob(positive test | infected)Prob(infected) + Prob(positive test| not infected)Prob(not infected = .90x.15 + .10x.85 = .22
Therefore, Prob(infected | positive test) = .90x.15/.22 = .6136

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