A test to determine whether a certain antibody is present is 99.7% effective. Th

Question

A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject). The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. Suppose the test is given to five randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all five people?
(b) What is the probability that the test comes back positive for at least one of the five people?

Explanation / Answer

X - no of tests that come back negative

X is Binomial with p =0.997, n = 5

a) P(X=5) = 0.9851

b) P(x>=1) = 0.999999.

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