Many people who come to clinics to be tested for HIV, the virus that causes AIDS

Question

Many people who come to clinics to be tested for HIV, the virus that causes AIDS, don't come back to learn the test results. Clinics now use "rapid HIV tests" that give a result while the client waits. The trade-off for fast results is that rapid tests are less accurate than slower laboratory tests. Applied to people who have no HIV antibodies, one rapid test has probability about 0.008 of producing a false positive (that is, of falsely indicating that antibodies are present).

If a clinic tests 200 people who are free of HIV antibodies, what is the probability that at least one false-positive will occur?

Explanation / Answer

The probability for negative result for any one person is =1-0.008=0.992

the probability that at least one false-positive will occur=1-P[no positive]

                                                                               = 1 - (0.992)^200

                                                                               = 0.7994

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