Question

In: Statistics and Probability

A new​ lie-detector test has been devised and must be tested before it is put into...

A new​ lie-detector test has been devised and must be tested before it is put into use. 200 people are selected at​ random, and each person draws and keeps a card from a box of 200 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who​ lied, 85​% fail the new​ lie-detector test​ (that is the test indicated​ lying). Of those who told the​ truth, 5​% 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?

A. What is the probability that a randomly chosen subject will have lied given that the subject failed the​ test? ​(Round to four decimal places as​ needed.)

B. What is the probability that the subject will not have lied given that the subject failed the​ test? ​(Round to four decimal places as​ needed.)

Solutions

Expert Solution

For A and B the probability of sample space S

P(A n B)= P(A) P(B|A)=P(B) P(A|B)

Let L is the event that person lied ,T be the event that person told truth and F is the person failed the li detectior test

P(L)=0.5

P(T)=0.5

P(F|L)=85%=0.85

P(F|T)=5%=0.05

(A) What is the probability that a randomly chosen subject will have lied given that the subject failed the​ test?

(B). What is the probability that the subject will not have lied given that the subject failed the​ test?

orchestra answered 1 year ago
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