Question

# The table below displays results from experiments with polygraph instruments. Find the positive predictive value for...

The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That​ is, find the probability that the subject​ lied, given that the test yields a positive result.

 Did the Subject Actually​ Lie?
 No​ (Did Not​ Lie) Yes​ (Lied) 1515 4040 3030 1212

The probability is?

​(Round to three decimal places as​ needed.)

Solution :

Given that

No​ (Did Not​ Lie) Yes​ (Lied) Total

Positive test results 1515 4040 5555

Negative test results 3030 1212 4242

Total 4545 5252 9797

put A = positive result , B = subject​ lied

=> we know that P(B/A) = P(A and B)/P(A)

= (4040/9797)/(5555/9797)

= 4040/5555

=> P(subject lied/positive result) = 0.727

=> The probability that the subject​ lied, given that the test yields a positive result is 0.727

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