Thread: Probability of a Lie Detector

Hey, Guys. I met a problems when I am doing the Statistics homework. I really need your helps. Thank you so much. The problem is :
There is a Lie Detector. In the Past experience, the accuracy rate tof the detectore is from 92% to 99%. To gain some insight into the risks that emplyees face when taking a lie detector test, suppose that the probability if .05 that a lie detector concludes that a person is lying who, in fact, is telling the truth and suppose that any pair of test are independent. What is the probability that a machine will conclude that :
a. each of three employees is lying when all are telling the truth?
b. at least one of the three employees is lying when all are telling the truth?
Thank you guys sooooo much !

Originally Posted by rabbitvivian

Hey, Guys. I met a problems when I am doing the Statistics homework. I really need your helps. Thank you so much. The problem is :
There is a Lie Detector. In the Past experience, the accuracy rate tof the detectore is from 92% to 99%. To gain some insight into the risks that emplyees face when taking a lie detector test, suppose that the probability if .05 that a lie detector concludes that a person is lying who, in fact, is telling the truth and suppose that any pair of test are independent. What is the probability that a machine will conclude that :
a. each of three employees is lying when all are telling the truth?
b. at least one of the three employees is lying when all are telling the truth?
Thank you guys sooooo much !

The number of false positives has a binomial distribution B(3,0.05)

CB

Thank you so much. But could you tell me how to get the answer?

CaptainBlack has already told you how to get the answer,

The distribution of the false positives is X~Binomial(3 , 0.5)

The first question asks you P(X=3), the second P(X>0).

Just use Binomial distribution - Wikipedia, the free encyclopedia

To compute those and you have your answer.