Question

In his book Chances: Risk and Odds in Everyday Life, James Burke states that there is a 72% 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. (Round your answers to one decimal place.)

(a) Suppose a person answers 90% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?
%

(b) Suppose a person answers 10% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?
%

(c) Repeat parts (a) and (b) if 40% of the questions are answered truthfully and 60% are answered with lies.

(a)	%
(b)	%

(d) Repeat parts (a) and (b) if 20% of the questions are answered truthfully and the rest are answered with lies.

(a)	%
(b)	%

Answer 1

Ans:

P(detect lie/lie)=0.72

P(detect lie/not lie)=0.07

a)P(not lie)=0.9,P(lie)=1-0.9=0.1

P(detect lie)=P(detect lie/lie)*P(lie)+P(detect lie/not lie)*P(not lie)

=0.72*0.1+0.07*0.9

=0.135

P(not detect lie)=1-0.135=0.865

P(lie/not detect lie)=P(not detect lie/lie)*P(lie)/P(not detect lie)=(1-0.72)*0.1/0.865=0.032 or 3.2%

b)

P(lie/detect lie)=P(detect lie/lie)*P(lie)/P(detect lie)=0.72*0.1/0.135=0.533 or 53.3%

c)P(lie)=0.6 ,P(not lie)=0.4

P(detect lie)=0.72*0.6+0.07*0.4

=0.46

P(not detect lie)=1-0.46=0.54

P(lie/not detect lie)=(1-0.72)*0.6/0.54=0.311 or 31.1%

P(lie/detect lie)=0.72*0.6/0.46=0.939 or 93.9%

d)P(lie)=0.8 P(not lie)=0.2

P(detect lie)=0.72*0.8+0.07*0.2

=0.59

P(not detect lie)=1-0.59=0.41

P(lie/not detect lie)=(1-0.72)*0.8/0.41=0.546 or 54.6%

P(lie/detect lie)=0.72*0.8/0.59=0.976 or 97.6%