5. Suppose that the prevalence of smoking among men in a region is 20%, and 0.4%

of men that smoke develop lung cancer. Answer the following questions:

(a) If two men are randomly selected, what is the probability that at least one of them is a smoker?

(b) If one man is randomly selected, what is the probability that he is a smoker and has lung cancer?

(c) If 0.1% of men in the region have lung cancer and one man is randomly selected, given that this man is a non-smoker, what is the probability that he has lung cancer?

(d) If one man is randomly selected, given that this man has lung cancer, what is the probability that he is a smoker?

(e) According to the definition of an independent event, demonstrate whether smoking and lung cancer are independent from each other using results obtained from the previous questions.