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a test to determine whether a certain antibody is present is 99.5% effective. this means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.5% of the time. the probability of a test coming back positive when the antibody is not present (a false positive) is 0.005. suppose the test is given to six randomly selected people who do not have the antibody.
A) what is the probability that the test comes back negative for all six people?
B) what is the probability that the test comes back positive for at least one of the six people?
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Since all tests come back negative, by the multiplication probability rule,
P(all 6 tests come negative) = 0.995^6= 0.97037 <--------
P(at least one test comes positive) will be the complement of the above probability, hence 1- 0.97037 =0.02963 <------
statistics and probability the worst subjects created by humans after calculus