A state health department reports a 5% rate of a certain virus for the \"at-risk

Question

A state health department reports a 5% 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 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 the initial screening? The probability that the at-risk subject has the virus is (Round to three decimal places as needed.)

Explanation / Answer

P(having virus if its know that they have tested positive)

= P(having virus | tested positive)

= P(having virus and tested positive)/P(tested positive) [P(A|B) = P(A and B)/P(B)]

= P(having virus and tested positive)/ (P(having virus and tested positive) + P(not having virus and tested positive))

= 0.05x0.99 / (0.05x0.99 + 0.95x0.01)

= 0.839

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