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.
Test result
+-
Antibodies present 0.9925 0.0075
Antibodies absent 0.003 0.997
Suppose that 5% of a large population carries antibodies to HIV in their blood.
(a) Draw a tree diagram for selecting a person from this population (outcomes: antibodies present or absent) and for testing his or her blood (outcomes: EIA positive or negative). (Do this on paper. Your instructor may ask you to turn in the work.)
(b) What is the probability that the EIA is positive for a randomly chosen person from this population?
(c) What is the probability that a person has the antibody given that the EIA test is positive?