Focus Problem: Expand Your Knowledge This problem continues the Focus Problem. The solution involves applying several basic probability rules and a little algebra to solve an equation.

(a) If the polygraph of Problem 32 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 5event detector indicates a lie. We are given P(B) 5 0.30. Let A 5event person is lying , so Ac 5event person is not lying. Then P B P A andB PA and B P B P A P B A PA P B A c

c c 5 1 5 1

( ) ( ) ( )

( ) ( ) ( | ) ( ) ( | )

Replacing P(Ac ) by 12P(A) gives P(B) 5P(A) ? P(B | A) 1[12P(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).

(b) If the polygraph indicated that 70% of the questions were answered with lies, what would you estimate for the actual percentage of lies?

AppendixLO1