According to the CDC men who smoke are 23 times more likely

According to the CDC, men who smoke are 23 times more likely to develop lung cancer than men who don\'t smoke. Also accroding to the CDC, 21.6% of men in the U.S. smoke. What is the probability that a man in the U.S. is a smoker, given that he develops lung cancer?

Solution

P(S) = 0.216, P(N) = 1 - P(S) = 0.784

& We have Men who smoke are 23 times more likely to develop lung cancer

P(C/S)/P(C/N) = 23
=> P(C/S) = 23 * P(C/N)

We required to find P(S/C)

P(S/C) = [ P(C/S)*P(S)] / [ P(C/S) * P(S) + P(C/N) P(N) ] = [ 23 * P(C/N) P(S) ] / [ 23 * P(C/N) P(S) +P(C/N)P(N) ]
= 23 P(S)/ 23 P(S)+P(N) = 23.0216 / 23.0216+0.784 = 4.968 / 5.572 - 0.8637