pring 2018-Quantitative Reasoning CAFE Section 17 Homework: Problem 5 Previous P

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pring 2018-Quantitative Reasoning CAFE Section 17 Homework: Problem 5 Previous Problem Problem List Next Problem (3 points) Polygraph tests have an accuracy rate of about 95%. This means that it will detect 95% of people who lie and 95% of people who are telling the truth. A company of 6000 employees has everyone submit to a polygraph test. It turns out there are 60 employees who will lie during their polygraph. (Hint: Tests Positive means they are lying!) Complete a table as in your course materials and use to answer the given question. If someone does not pass their polygraph test, what is the probability they lied? (Round your probability to the nearest tenth of a percent!) Express your answer rounded correctly to the nearest tenth of a percent. Probability if you haven't answered the question correctly in 3 attempts, you can get a hint. Preview My AnswersSubmit Answers Show me another

Explanation / Answer

The problem tells us that P(Liar) = 60/6000 = 0.01 and P(Positive | Liar) = 0.95.

P(Positive) = (0.01)(0.95) + (0.99)(0.05) = 0.059

Using Bayes Rule ,

P(Liar |Positive) = P(Positive | Liar)*P(Liar) /P(Positive) = (0.95)(0.01)/ (0.059) = 0.161 = 16.1%

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