Question

A new​ lie-detector test has been devised and must be tested before it is put into use. Three hundred people are selected at​ random, and each person draws and keeps a card from a box of 300 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who​ lied, 90​% fail the new​ lie-detector test​ (that is the test indicated​ lying). Of those who told the​ truth, 6​% failed the test. What is the probability that a randomly chosen subject will have lied given that the subject failed the​ test? That the subject will not have lied given that the subject failed the​ test?

Answer 1

P(failed the test)=P(telling true)*P(failed the test|telling true)+P(telling lie)*P(failed the test|telling lie)
=0.5*0.06+0.5*0.9=0.48

1)

probability that a randomly chosen subject will have lied given that the subject failed the​ test

=0.5*0.9/0.48 =0.9375

2)

P( subject will not have lied given that the subject failed the​ test)

=0.5*0.06/0.48 =0.0625