00:01
It's stated in this question that polygraph tests accurately identify liars 90 % of the time, but also say that a truthful person is lying 50 % of the time.
00:15
So we can write this as follows.
00:17
The probability of testing positive for lying, given that the person is lying, is 90 % or .90.
00:28
And the second half of the sentence says the probability of testing positive for lying, given that the person is telling the truth, is 50 % or .50.
00:42
Now we consider 100 suspected criminals, of whom 700 are telling the truth when given a polygraph.
00:50
So we can say that among these suspected criminals, the probability that they are telling the truth is 700 out of 1000 or .7.
01:02
We are asked, what is the probability that a person is telling the truth, given that the lie detector has tested positive? so this is a conditional probability.
01:13
What is the probability that the person is telling the truth, given that they tested positive for lying? and to answer this question, we can make use of bayes ' theorem.
01:30
And bayes ' theorem basically says, probability of event b, given event a, is equal to the probability of a given b, times the probability of b, divided by the probability of a.
01:47
So for our scenario, we can express this as the probability of testing positive, given that you're telling the truth, times the probability of telling the truth, divided by the probability of testing positive.
02:05
Now we have this probability already given to us in the question.
02:09
It's .5...