In his book Chances: Risk and Odds in Everyday Life, James Burke states that the
ID: 3208126 • Letter: I
Question
In his book Chances: Risk and Odds in Everyday Life, James Burke states 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. (Round your answers to one decimal place.) Suppose a person answers 88% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies? % Suppose a person answers 12% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies? % Repeat parts (a) and (b) if 53% of the questions are answered truthfully and 47% are answered with lies. % % Repeat parts (a) and (b) if 20% of the questions are answered truthfully and the rest are answered with lies. % %Explanation / Answer
Solution:
a. p(wrongly detected a lie) = p(person tells truth) * p(machine says lie | person tells truth) = 0.88 * 0.07 = 0.0616
b. p(correctly detected a lie) = p(person tells lie) * p(machine says lie | person tells lie) = 0.12 * 0.72 = 0.0864
c. Repeat with p(person tells truth) = 0.53 and p(person tells lie) = 0.47
d. Repeat with p(person tells truth) = 0.20 and p(person tells lie) = 0.80
Note all these answers need to be multiplied by 100 to be turned into percentages. i.e 0.0616 = 6.16%, etc.