Answer to Question #167316 in Statistics and Probability for Moses Thairu

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.

No_(Did_Not_Lie) Yes_(Lied)

Positive_test_results 14 43

Negative_test_results 34 12

Answer 1

$P(subject\; lied|test\;yields \;a \;positive\; result) = \frac{P(subject \; lied \; and \; the \; test \; yields \; a \; positive \; result)}{P(the\; test\; yields \;a \;positive\; result)} \\ = \frac{\frac{43}{103}}{\frac{57}{103}} = \frac{43}{57} = 0.754$