Risk and Odds in Everyday Life. Burke states that there is a 72% chance a polygr

Question

Risk and Odds in Everyday Life. 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.) (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 win the polygraph correctly indicate are lies? (C) Repeat parts (a) and (b) if 55% of the questions are answered truthfully and 45% are answered with lies. a) 0.55% b) 32% (d) Repeat parts (a) and (b) if 15% of the Questions are answered truthfully and the rest are answered with lies. a) % b) %

Explanation / Answer

Given polygraph detects 72% detects lie if he lies

7% gives as lie even if he doesn't lie

a) probability of person truth = 0.9

% of answers will polygraph wrongly indicate lie = 0.07*0.9*100 = 0.063*100= 6.3%

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b) probability of person lying = 0.1

% of answwrs will polygraph correctly indicate lies = 0.72*0.1*100 = 7.2%

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c) 55% truthful, 45% lies

(a) 0.07 * 0.55 * 100 = 3.85%

(b) 0.72 * 0.45 * 100 = 32.4%

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d) 15% truthful, 85% lies

(a) 0.07* 0.15 * 100 = 1.05%

(b) 0.72* 0.85 * 100 = 61.2%

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