Answer to Question #143916 in Statistics and Probability for Vladimyr Lubin

Question

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)
Positive test results 20 40
Negative test results 32 11

The probability is (Round to 3 decimals)

Answer 1

$P(subject \; lied\;/test \;yields\; a \;positive\; result) = \frac{P(subject \; lied \; and \; the \; test \; yields \; a \; positive \; result)}{P(the\; test\; yields \;a \;positive\; result)}$

$= \frac{\frac{43}{103}}{\frac{60}{103}} = \frac{43}{60} = 0.716$