2. Prostate cancer is the most common form of cancer among men. Over a lifetime. there is a 16% probability that a man develops prostate cancer. That probability increases with age as shown in the table below. Age group Probability of Prostate Cancer 40 below 50 0.010 50 below 60 0.022 60 and above 0.125 0.157 A PSA test, a blood test that measures the level of a certain protein produced by the prostate, is used as an indicator of this cancer. This test, however, has a low accuracy and would still require a biopsy for conrmation. Of those with cancer, there is a 30% probability that it is not detected (false negative) while for those without cancer. there is a 13.5% probability that the test shows positive for cancer (false positive). a. Determine the probability that a 56-year-old man will have a positive PSA test result? b. If this man tests positive for PSA, what is the probability that he really has cancer? 0. For every 100,000 men of age 50-60, how much should be the budget for biopsy in case the government will include it as a health benefit? Each biopsy procedure for those that tested positive is P2000