Question: 3. U.S. Customs and Border Protection has been testing automated kiosks that may be able to detect lies. One measurement used (among several) is involuntary

3.

U.S. Customs and Border Protection has been testing automated kiosks that may be able to detect lies. One measurement used (among several) is involuntary eye movements. Using this method alone, tests show that it can detect 60% of lies, but incorrectly identifies 15% of true statements as lies. Suppose that 95% of those entering the country tell the truth. The immigration kiosk asks questions such as "Have you ever been arrested for a crime?" Naturally, all the applicants answer "No," but the kiosk identifies some of those answers as lies, and refers the entrant to a human interviewer.

SHOW WORK FOR THESE.

a) Here is the outline of a probability tree for this situation. Fill in the probabilities:

b) What is the probability that a random person will be telling the truth and will be cleared by the Kiosk?

c) What is the probability that a random person will be telling a lie and will be discovered to be lying by the Kiosk?

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