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. Find the probability that the person:
a) was a heavy smoker
b) has lung cancer given the person was a moderate smoker
c) has lung cancer given the person was a non-smoker.