12% of the over-60 population of Agento have lung cancer. Of those with lung cancer, 50% were heavy smokers, 40% were moderate smokers, and 10% were non-smokers. Of those without lung cancer, 5% were heavy smokers, 15% were moderate smokers, and 80% were non-smokers.
A member of the over-60 population of Agento is chosen at random.
a. Find the probability that the person was a heavy smoker.
b. Given the person was a moderate smoker, find the probability that the person has lung cancer.
c. Given the person was a non-smoker, find the probability that the person has lung cancer.