Calculation practice: General multiplication rule. In the 1980s in Canada, 52% of adult men smoked. It was estimated that male smokers had a lifetime probability of 17.2% of developing lung cancer, whereas a nonsmoker had a 1.3% chance of getting lung cancer during his life (Villeneuve and Mao 1994).

a. What is the conditional probability of a Canadian man getting cancer, given that he smoked in the 1980s?

b. Draw a probability tree to show the probability of getting lung cancer conditional on smoking.

c. Using the tree, calculate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer.

d. Using the general multiplication rule, calculate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. Did you get the same answer as in (c)?

e. Using the general multiplication rule, calculate the probability that a Canadian man in the 1980s both did not smoke and never contracted lung cancer.