One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a 0.04 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is 0.85, and the probability of a false-negative (no indication of cancer when cancer is actually present) is 0.30. Let C = event male patient has prostate cancer + positive PSA test for prostate cancer - negative PSA test for prostate cancer. What is the probability that the male patient has prostate cancer and the PSA test comes back false negative?
0.843
0.012
0.124
0.363