A researcher says that there is a 73% chance a polygraph test (lie detector test

Question

A researcher says that there is a 73% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 6% chance that the polygraph will falsely accuse someone of lying. (a) If the polygraph indicated that 31% 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) = 0.31. Let A = event person is lying, so Ac = event person is not lying. Then PLB) = p(A and B) + P(A and B) P(B) P(A)P(B I A) P(A )P(B | AC) Replacing P(A) by 1 -P(A) gives into the last equation and solve for P(A). (Round your answer to two decimal places.) Substitute known values for P(B), P(B I A), and P(BI A P(A) = | (b) If the polygraph indicated that 69% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)

Explanation / Answer

a) here P(B) =P(A)*P(B|A)+P(Ac)*P(B|Ac)

0.31 =P(A)*0.73+(1-P(A))*0.06

0.25 =0.67*P(A)

P(A) =0.25/0.67 =0.37

b)

from above estimated % of lies =94.0%

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