A researcher says that there is a 77% 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 30% 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) = 0.30. Let A = event person is lying, so Ac = event person is not lying. Then

P(B) =P(A and B) + P(AcandB)

P(B) = P(A)P(B | A) + P(Ac)P(B|Ac)

Replacing P(Ac)by1−P(A) gives P(B)=P(A)⋅P(B)1−P(A)]⋅P(B|Ac)

Substitute known values for P(B), P(B | A), and P(B|Ac) into the last equation and solve for P(A). (Round your answer to two decimal places.)

P(A) =

(b) If the polygraph indicated that 67% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)