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 19 40
negative test results 30 12
the probability is
(round to three decimal places as needed.)

Explanation:

Step1: Identify relevant values

Positive - test results and lied: 40. Positive - test results total: \(19 + 40=59\).

Step2: Calculate probability

The probability \(P\) that the subject lied given a positive - test result is the number of positive - test results and lied divided by the total number of positive - test results. So \(P=\frac{40}{19 + 40}\).

Answer:

\(\frac{40}{59}\approx0.678\)