2.25 A polygraph (lie detector) is said to be 90% re/able in the following sense
ID: 3072014 • Letter: 2
Question
2.25 A polygraph (lie detector) is said to be 90% re/able in the following sense: There is a 90% chance that a person who is telling the truth will pass the polygraph test; and there is a 90% chance that a person telling a lie will fail the polygraph test. (a) suppose a population consists of 5% liars. A random person takes a polygraph test, which concludes that they are lying. What is the probability that they are actually lying? (b) Consider the probability that a person is actually lying given that the poly-graph says that they are. Using the definition of reliability, how reliable must the polygraph test be in order that this probability is at least 80%?Explanation / Answer
a)P(test said lying)=P(lying in actual and test said lying)+P(not lying in actual and test said lying)
=0.05*0.9+(1-0.05)*(1-0.9)=0.14
hence P(actually lying given test conclude lying)
=P(lying in actual and test said lying)/P(test conclude lying) =0.05*0.9/0.14 =0.321429
b)
let relaibility =R
hence P(actually lying given test conclude lying)=0.05*R/(0.05*R+(1-0.05)*(1-R))>=0.80
0.05R>=0.80*(0.95-0.90R)
0.05R >=0.76-0.72R
0.77R >=0.76
R>=0.76/0.77
R>=76/77
R>=0.9870 ~ 98.70%
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