申論題

4.(10%) One of the most common tests for the detection of prostate cancet is the prostate-specific antigen (PSA) test. Suppose there is a 0.23 probability that a male patient has prostate cancer before testing. The probability of a false-positive (tests that come back positive for cancer when no cancer is present) for the SPA test is 0.65, and the probability of a false-negative (no indication of cancet when cancer is actually present) is 0.18.

(a) What is the probability that the male patient has prostate cancer if the PSA test comes back negative? (5%)