Colon and rectal cancer, sometimes called Colorectal cancer, is the 2^nd leading cause of cancer death in men. Its rate has been falling by 2% per year. Much of its decline can be explained by early and better detection. Ninety percent of diagnosed cases of male colorectal cancer occur in men 50 and over. Two percent of men aged 50 to 60 in the US will get colorectal cancer. (treat this last stat as the population probability)

Men are highly encouraged aged 50 and older to receive yearly colorectal cancer screenings. This usually includes a colonoscopy, a flexile signoidoscopy, and a fecal occult blood test. If a man has colorectal cancer, the probability is 90% that he will have a positive colorectal screening. If a man does not have colorectal cancer, the probability of a positive screening is 5%.

a). If a man has colorectal cancer, what is the probability that he would have three consecutive negative colorectal screenings?

b). If a man aged 50 or more has a positive colorectal screening, what is the probability that he actually has this cancer?

c). Last year 52,000 American died from Colorectal Cancer of the 155,000 diagnosed cases. Eighty percent of those who died did not have yearly colorectal screenings after age 50. Last year, 50% of men in the US aged 50 and over had colorectal screenings. Discuss with words and perhaps statistics how there is room for further reduction in colorectal deaths.