Answer: Choice D) 0.07
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Work Shown:
- S = person is a smoker
- LC = person has lung cancer
- P(S) = 0.31 = probability someone is a smoker
- P(LC given S) = probability someone has lung cancer, given they are a smoker
- P(LC given S) = 0.226
Use that given info to say the following:
P(LC given S) = P(LC and S)/P(S)
P(LC and S) = P(LC given S)*P(S)
P(LC and S) = 0.31*0.226
P(LC and S) = 0.07006
P(LC and S) = 0.07
This problem is an example of using conditional probability.
I used "and" in place of the intersection symbol
Saying P(LC and S) is the same as P(S and LC). The order doesn't matter.