Math Help - Probability help please

Q: A study of the residents of a region showed that 20% were smokers. The probability 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 .006, what is the probability of death due to lung cancer given that the person is a smoker?

I tried to use Baye's rule, but had not luck. How do I make use of the fact that P(D|S)=10P(D|S'), where D represents deaths due to lung cancer and S is for smokers.

Thanks

2. Originally Posted by Danneedshelp
Q: A study of the residents of a region showed that 20% were smokers. The probability 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 .006, what is the probability of death due to lung cancer given that the person is a smoker?

I tried to use Baye's rule, but had not luck. How do I make use of the fact that P(D|S)=10P(D|S'), where D represents deaths due to lung cancer and S is for smokers.

Thanks
Hint: P(D) = P(D|S) P(S) + P(D|S') P(S')

3. Originally Posted by awkward
Hint: P(D) = P(D|S) P(S) + P(D|S') P(S')
How do I use that for this problem? I set up a box with all the information, but i am still not getting the desired 0.21 as my answer.

4. Originally Posted by Danneedshelp
Q: A study of the residents of a region showed that 20% were smokers. The probability 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 .006, what is the probability of death due to lung cancer given that the person is a smoker?

I tried to use Baye's rule, but had not luck. How do I make use of the fact that P(D|S)=10P(D|S'), where D represents deaths due to lung cancer and S is for smokers.

Thanks
Draw a tree diagram. The first two branches are S (smokes) and S' (does not smoke). From each of those two branches there are two more branches. The first branch is D (death) and the second branch is D' (no death).

Let Pr(D | S') = x. Then Pr(D | S) = 10x.

From the tree diagram: $0.006 = (0.2)(10x) + (0.8)(x)$. Solve for $x$ and substitute into Pr(D | S) = 10x.