Refer to Exercise 85. Many of the positive results from EIA tests are false positives. It is therefore common practice to perform a second EIA test on another blood sample from a person whose initial specimen tests positive. Assume that the false positive and false negative rates remain the same for a person’s second test. Find the probability that a person who gets a positive result on both EIA tests has HIV antibodies.

Exercise 85.

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:

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Test result Antibodies present 0.9985 0.0015 Truth Antibodies absent 0.0060 0.9940