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? Did the Subject Actually​ Lie?   Positive test result No ( did not lie) 20, Yes (lied) 42 Negative test results No ( did not lie) 32, Yes (lied) 9  The probability is

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