Among male smokers, the lifetime risk of developing lung cancer is 17%; among female smokers, this risk is 12%. For nonsmokers, this risk is significantly lower:

1.3% for men and 1.5% for women. Assuming equal numbers of men and women in the general population, find the probability that

(i) a man who develops lung cancer is a nonsmoker;

(ii) a woman who develops lung cancer is a smoker;

(iii) a person who develops lung cancer is a smoker.