Confusion of the Inverse 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). (Hint: Assume that the study involves 1000 sub jects and use the given information to construct a table with the same format as Table.)
b. Find P (positive test result | malignant). (Hint: Assume that the study involves 1000 sub jects and construct a table with the same format as Table.)
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?