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.