Exercise from lecture: The CIA and FBI use polygraph machines (lie detectors) to

Question

Exercise from lecture: 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

A) Total number of people who will fail the test if 10,000 are tested = 1600+8 = 1608

So, P(a person fails test) = 1608/10000 = 0.1608

B) P(spy | fail the test) = P(spy and fails)/P(fail the test)

= (8/10,000)/(1608/10,000) = 0.004975

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