In his book Chances: Risk and Odds in Everyday Life , James Burke states that th
ID: 3126867 • Letter: I
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 54% of the questions are answered truthfully and 46% are answered with lies.
(d) Repeat parts (a) and (b) if 19% of the questions are answered truthfully and the rest are answered with lies.
Explanation / Answer
when person lie it is detected correctly by 72%
when person lie it is not detected correctly by 28%
when someone say truth, it is detected as truth by 93%
when someone say truth it is detected false by 7%
a)90% of times he said truth
so the probability his answer will be wrongly detected as false = 0.9*0.07 = 0.063
= 6.3%
b)person answered 10% question as false
now the probability that these are correctly detected = 0.72*0.10 = 0.072
= 7.2%
c) 1) if 54% answered correctly
then wrongly detetced as false = 0.54*0.07 = 0.037
= 3.7%
2) 46% are answered as lies
therefore correctly indicated as false = 0.46*0.72 = 0.3312
= 33.12%
d) 1) he answered 19% right, therefore wrongly detected as false = 0.19*0.07 = 0.0133
= 1.33%
2) if 81% are false then those are correctly detetected = 0.81*0.72 = 0.5832
= 58.32%