Question 426048
you are given:

.85 of those developing lung cancer are smokers.
.16 of the population developed lung cancer.


this means that .85 * .16 = .136 of the population developed lung cancer and also smoked.


the smokers, however, only make up .45 of the population.


this means that .136 / .45 = .302222222 of the smokers developed lung cancer.


the probability that a smoker in this population will develop lung cancer is equal to .302222222


this is a p(a given b) type problem.


p(a given b) = p(a intersect b) / p(b)


p(b) is the probability that a person is a smoker.


p(b) equals .45


p(a intersect b) is the probability that a person has lung cancer is also a smoker.


since the probability that the person has lung cancer is .16 and the probability that the person who has lung cancer also smokes is .85, then:


p(a intersect b) = .16 * .85 = .136


p(a given b) = p(a intersect b) / p(b) = .136 / .45 = .3022222222


if you are a smoker in this population, then the probability that you will have lung cancer is .302222


this is based on the previous experience that indicates that .30222222 of the persons in the population who smoked also developed lung cancer.