A survey of people in a given region showed that 20 were smo

A survey of people in a given region showed that 20% were smokers. The probability of death due to lung cancer, given that a person smoked, was roughly 10 times the probability of death due to lung cancer, given that a per son did not smoke. If the probability of death due to lung cander in the region is 0.006, what is the probability of death due to lung cancer given that a 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)