Question

A researcher says that there is a 71% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 9% 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 $A^c$ = event person is not lying. Then $P(B) = P(A \text{ and } B) + P(A^c \text{ and } B)$ $P(B) = P(A)P(B|A) + P(A^c)P(B|A^c)$ Replacing $P(A^c)$ by $1 - P(A)$ gives $P(B) = P(A) \cdot P(B|A) + [1 - P(A)] \cdot P(B|A^c)$ Substitute known values for $P(B)$, $P(B|A)$, and $P(B|A^c)$ into the last equation and solve for $P(A)$. (Round your answer to two decimal places.) P(A) = (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.) %

          A researcher says that there is a 71% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 9% 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 $A^c$ = event person is not lying. Then
$P(B) = P(A \text{ and } B) + P(A^c \text{ and } B)$
$P(B) = P(A)P(B|A) + P(A^c)P(B|A^c)$
Replacing $P(A^c)$ by $1 - P(A)$ gives
$P(B) = P(A) \cdot P(B|A) + [1 - P(A)] \cdot P(B|A^c)$
Substitute known values for $P(B)$, $P(B|A)$, and $P(B|A^c)$ into the last equation and solve for $P(A)$. (Round your answer to two decimal places.)
P(A) = 
(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.)
%

A researcher says that there is a 71% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 9% 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 $A^c$ = event person is not lying. Then
P(B) = P(A and B) + P(A^c and B)
P(B) = P(A)P(B|A) + P(A^c)P(B|A^c)
Replacing P(A^c) by 1 - P(A) gives
P(B) = P(A) · P(B|A) + [1 - P(A)] · P(B|A^c)
Substitute known values for P(B), P(B|A), and P(B|A^c) into the last equation and solve for P(A). (Round your answer to two decimal places.)
P(A) =
(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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