A study of the residents of a region showed that 20 were smo

A study of the residents of a region showed that 20% were smokers. The chance of death due to lung cancer, given that a person smoked, was ten times the probability of death due to lung cancer, given that the person did not smoke. If the probability of death due to lung cancer in the region is 0.06, what is the probability of death due to lung cancer, given the person is a smoker?

Solution

S: Person smoked

D: Person died of lung cancer

P(S) = .20, so P(not S) = .80

P(D given S) = 10*P(D given not S), so P(D given not S) = .1*P(D given S)

P(D) = .006

P(D) = P(S)*P(D given S) + P(not S)*P(D given not S)

.006 = .20*P(D given S) + .80*.1*P(D given S)

.006 = . 28*P(D given S)

P(D given S) = .02143 (answer)