Smoking and Cancer

You tell me smoking causes lung cancer. I know several of my friends who smokes but never got cancer. How do you explain?

Suppose 90% of lung cancer patients are smokers and 20% of people with no lung cancer also smoke. What is the chance that a smoker has cancer? To estimate the answer, we should first know the probability of lung cancer in society. Suppose it is 0.1%.

$\\ P(LC|S) = \frac{P(S|LC)*P(LC)}{P(S|LC)*P(LC) + P(S|nLC)*P(nLC)} \\ \\ \frac{0.9*0.001}{0.9*0.001 + 0.2*0.999} = 0.004484305$

So, the probability of a random smoker having cancer is 0.44%. So what about non-smokers having lung cancer?

$\\ P(LC|nS) = \frac{P(nS|LC)*P(LC)}{P(nS|LC)*P(LC) + P(nS|nLC)*P(nLC)} \\ \\ \frac{0.1*0.001}{0.1*0.001 + 0.8*0.999} = 0.0001251095$

It is 0.013%. Therefore, a smoker is 0.44/0.013 = 35 times more likely to get cancer.

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