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].

1) A person is selected at random, what is the probability that the person fails the test? 2) Suppose a person fails the test, what is the probability that the person is a spy?

please answer in detail and show all steps for solveing by good handwriting

Explanation / Answer

1) P(a person failed) =Totalnumber of people failed / total number of people tested = (1600 + 8)/10000 = 0.1608

2) P(spy | a person failed) = P(spy failing)/p(failing)

= (8/10,000)/(0.1608) = 0.004975

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