In this problem, you are asked to solve part of the Focus Problem at the beginning of this chapter. In his book Chances: Risk and Odds in Everyday Life, James Burke says that there is a 72% chance a polygraph test (lie-detector test) will catch a person who is in fact lying. Furthermore, there is approximately a 7% chance that the polygraph will falsely accuse someone of lying.
(a) Suppose a person answers 90% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?
(b) Suppose a person answers 10% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?
(c) Repeat parts (a) and (b) if 50% of the questions are answered truthfully and 50% are answered with lies.
(d) Repeat parts (a) and (b) if 15% of the questions are answered truthfully and the rest are answered with lies.