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. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV. (Centers for Disease Control and Prevention, 1998.)
Test Result
+ -
Antibodies present 0.9985 0.0015
Antibodies absent 0.006 0.994
Suppose that 1% of a large population
carries antibodies to HIV in their blood.
a. Blood donors are prescreened for HIV risk factos, so perhaps only 0.1% (0.001) of this population carries HIV antibodies. Find the probability that a person from this population has the antibody given that the EIA test is positive.
b. Clients of a drug rehab clinic are a high-risk group, so perhaps 10% of this population carries HIV antibodies. Find the probability that a person from this population has the antibody given that the EIA test is positive.
c. What general lesson do your calculations illustrate?