A screening test which measures the level of a prostate speific antigen (PSA) is a commonly used tool for the detection of prostate cancer. Men with PSA levels greater than 10 have a chance of 67% of prostate cancer, whereas men whose PSA levels are between 4 an 10 have a 25% chance of having prostate cancer. For those whose PSA levels were lower than 4 there chance is only 5%. Suppose that 15% of men have PSA levels greater than 10, 10% of men PSA levels between 4 and 10 and 75% of men have PSA levels lower than 4.
a. What is the probability that a radnomly chosen man will develop prostate cancer?
b. What is the probability that a randomly chosen man hads a PSA level greater than 10, given that he has prostate cancer?