In one study, physicians were asked to estimate the probability of a malignant cancer given that a test showed a positive result. They were told that the cancer had a prevalence rate of 1%, the test has a false positive rate of 10%, and the test is 80% accurate in correctly identifying a malignancy when the subject actually has the cancer. (See Probabilistic Reasoning in Clinical Medicine by David Eddy, Cambridge University Press.)

a.Find P(malignant | positive test result).

b.Find ^(positive test result | malignant).

c.Out of 100 physicians, 95 estimated P(malignant | positive test result) to be about 75%. Were those estimates reasonably accurate, or did they exhibit confusion of the inverse? What would be a consequence of confusion of the inverse in this situation?