The most common HIV test is the Enzyme Immunoassay (EIA) Test. When a subject’s HIV condition is known, the following probabilities about the EIA test are known.

Pr(Test(+) I HIV(+)) = 0.9985

Pr(Test(-) I HIV(-)) = 0.994

(a) Find Pr(Test(-) I HIV(+)), the probability of a false negative.

(b) Find Pr(Test(+) I HIV(-)), the probability of a false positive.

(c) Suppose that in the U.S. population, Pr(HIV(1)) = 0.01.

Testing the general population would be effective (both in terms of diagnosis and costs) if a positive test could pinpoint the disease. If a randomly selected person is given the EIA Test, calculate Pr(HIV(+) I Test(+)) and Pr(HIV(-) I Test(+)).

(d) Do the answers from part (c) suggest that testing the general population would be effective? Explain.