A researcher says that there is a 78% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 5% chance that the polygraph will falsely accuse someone of lying. (a) If the polygraph indicated that 35% 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) = 0.35. 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(Ac)P(B | Ac) Replacing P(Ac) by 1 − P(A) gives P(B) = P(A) · P(B | A) + [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 65% 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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A researcher says that there is a 78% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 5% chance that the polygraph will falsely accuse someone of lying.

(a) If the polygraph indicated that 35% 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) = 0.35. 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(Ac)P(B | Ac)

Replacing P(Ac) by 1 − P(A) gives

P(B) = P(A) · P(B | A) + [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 65% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)
%