Calculation practice: Bayes’ theorem. Refer to Practice Problem 4. Use the following steps to calculate the probability that a Canadian man smoked, given that he had been diagnosed with lung cancer.

a. Write Bayes’ theorem for the specific case described in this question.

b. Calculate the probability that a Canadian man in the late 1980s would eventually develop lung cancer. (Use the law of total probability.)

c. Use Bayes’ theorem to calculate the probability that a man from this population smoked, given that he eventually developed lung cancer.

Data from problem 4

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).