A diagnostic test for the presence of the AIDS virus has probability 0.005 of pr

Question

A diagnostic test for the presence of the AIDS virus has probability 0.005 of producing a false positive. That is, when a person free of the AIDS virus is tested, the test has probability of 0.005 of falsely indicating that the virus is present. If the 140 employees of a medical clinic are tested and all 140 are free of the virus, what is the probability that at least one false positive will occur?

You may assume that test results for different individuals are independent.

a.0

b.0.3487

c.0.4957

d.0.5043

e.0.7

The answer is D, please explain the process and why

Explanation / Answer

probabilty that at least one false positive =1-P(none of them false positive)

=1-(1-0.005)140 =1-0.4957=0.5043

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