A Canadian male has recently had a Prostate Specific Antigen (PSA) test as to determine if he has prostate cancer. The false-positive rate of a PSA test is 14%. If he does have prostate cancer, PSA test will be positive 80% of the time.

Because this male is showing symptoms that are consistent with prostate cancer, it is assumed that the chance he has prostate cancer prior to taking the PSA test is 0.17.

Part (a) What is the probability that the PSA test will yield a positive result, confirming that he does have prostate cancer?

Part (b) If the PSA test gives a positive result, what is the probability that he does not have prostate cancer?

Part (c) Suppose the PSA test result is negative, indicating that he does not have prostate cancer and his symptoms are a result of something else. What is the probability that he does have prostate cancer?