A screening test which measures the level of a prostate specific antigen (PSA) is a commonly usedtool for the detection of prostate cancer. Men with PSA levels greater than 10 (ng/ml) have a chance of 67% ofprostate cancer, whereas men whose PSA levels are between 4 and 10 have a 25% chance of having prostate cancer.For those whose PSA levels are below 4, the risk of developing prostate cancer is only 5%. Suppose that 15% of menhave PSA levels greater than 10, 10% of men have PSA levels between 4 and 10, and 75% of men have PSA levelslower than 4.

(a) What is the probability that a randomly chosen man will develop prostate cancer?