U.S. Customs and Border Protection have 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 €œHave you ever been arrested for a crime?€ Naturally, all the applicants answer €œNo,€ but the kiosk identifies some of those answers as lies, and refers the entrant to a human interviewer.
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 person who is rejected by the kiosk was actually telling the truth?

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