Lie detector suits

Tree diagrams and conditional probability

PROBLEM:

In a 2012 interview with CBS News, Tom Hanks said that "80% of the population are really

great, caring people who will help you and tell the truth. And I think 20% of the population

are crooks and liars." A new lie detector suit has been tested and was sho

wn to correctly

identify truthful people 88.9% of the time and correctly identify liars 75.6% of the time. A

positive test is one in which the person is identified as a liar and a negative test is one in

which the person is identified as truthful. Sometimes, the test suggests that a truthful

person is a liar (a "false positive"); other times, the test indicates that a liar is being truthful

(a "false negative").

Assume that Tom Hanks and the company that makes the lie detector suit are telling the

truth. A randomly selected person from the population tests positive for being a liar. Find

the probability that this person is a liar.