Question: Enzyme-linked immunosorbent assay (ELISA) is the most common type of screening test for detecting the HIV virus. A positive result from an ELISA indicates that the HIV virus is present. For most populations, ELISA has a high degree of sensitivity (to detect infection) and specificity (to detect noninfection). (See HIVInsite, at www.HIVInsite.ucsf.edu.) Suppose that the probability a person is infected with the HIV virus for a certain population is 0.015. If the HIV virus is actually present, the probability that the ELISA test will give a positive result is 0.995. If the HIV virus is not actually present, the probability of positive results from an ELISA is 0.01. If the ELISA has given a positive result, use Bayes’ theorem to find the probability that the HIV virus is actually present.
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