A researcher says that there is a 80 chance a polygraph test lie detector test will catch a person who is in fact lying

Question

A researcher says that there is a 80 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 If the polygraph indicated that 36 of the questions were answered with lies what would you estimate for the actual percentage of lies in the answers Hint Let B event detector indicates a lie We are given P B 0 36 Let A event person is lying so AC event person is not lying Then P B P A and B P AC and B P B P A P B A P A P BA Replacing P A by 1 P A gives P B P A P B A 1 P A P B A Substitute known values for P B P BIA and P B A into the last equation and solve for P A Round your answer to two decimal places P A x b If the polygraph indicated that 64 of the questions were answered with lies what would you estimate for the actual percentage of lies Round your answer to one decimal place

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