The CIA and FBI use polygraph machines (lie detectors) to screen job applicants.

Question

The CIA and FBI use polygraph machines (lie detectors) to screen job applicants. A review by a federal panel of scientists reported that "if polygraphs were administered to a group of 10000 people that included ten spies, 1600 innocent people would fail the test and two spies would pass." [Source: Washington Post, May 1, 2006]. A person is selected at random, what is the probability that the person fails the test? Suppose a person fails the test, what is the probability that the person is a spy?

Explanation / Answer

as total number of people who falis the test =1600+8=1608

hence probability that person fails the test =1608/10000=0.1608

b)as 8 out of 10 fail the test given they are spy

probabilty that person is spy, given fails the test =8/1608=0.004975

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