Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. A false positive occurs when the test gives a positive result but no HIV antibodies are actually present in the blood. A false negative occurs when the test gives a negative result but HIV antibodies are present in the blood. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV:

Suppose that 1% of a large population carries antibodies to HIV in their blood. Imagine choosing a person from this population at random. If the person’s EIA test is positive, what’s the probability that the person has the HIV antibody?

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Test result Antibodies present 0.9985 0.0015 Truth Antibodies absent 0.0060 0.9940