Question

Assume that the probability of developing lung cancer in smokers is 15%; the probability of developing lung cancer in non-smokers is 1%; and the prevalence of smokers in the U.S. is 20%. If a person is diagnosed with lung cancer, what is the probability that he/she is a smoker?

Answer 1

Answer:0.789

Explanation:

20 % person smokes and 80 % don't smoke

Probability that a smoker gets lung cancer=15%

Probability that a non smoker gets lung cancer is =1%

Thus

Probability if a person is diagnosed with cancer he/she is a smoker

P=
`(Smoker)/(Given he gets cancer)`

P=
`(0.2* 0.15)/(0.8* 0.01+0.2* 0.15)`

P=
`(0.03)/(0.038)`=0.789