Question

Researchers estimate that 21.5% of men and 17% of women smoke. 70.2/100000 men develop lung cancer and 50.5/100000 women 90% of men who have lung cancer are smokers and 80% of women Given that a man has lung cancer, what is the probability that he is a smoker? Write this event with the correct conditional notation.

Answer 1

All the probabilities are given for the three different scenarios in men and women: people who smoke, people who develop lung cancer, and people who develop lung cancer who are also smokers. Then, these are even classified in terms of gender.

But the final question only has to do with men who are smokers that develop lung cancer. So, I think all the other data are only there for the purpose of red herring. The answer is already there, but you just have to find it among the others. First, you ignore all the probabilities involving women because we only want the men. Then, you find the probability of men that have lung cancer being smokers. The answer is 90%.