4. In a region, 12% of the adult population are smokers, 0.8% are a smoker with

Question

4. In a region, 12% of the adult population are smokers, 0.8% are a smoker with
emphysema, and 0.2% are nonsmokers with emphysema.

a. What is the probability that a person selected at random has emphysema?
b. Given that the selected person is a smoker, what is the probability that this
person has emphysema?
c. Given that the selected person is not a smoker, what is the probability that
this person has emphysema?
(Hint: For the selected person , denote the events A : Smoker and B : has
emphysema).

Explanation / Answer

a) add the probabilities together, .2% and .8%, equals 1% .01 b) .8% of the whole population would equate to 6.6% of the 12% who smoke. this is from dividing .8 by 12 .066666666 c) .2% of the whole population equates to .227% of the 88% who do not smoke. this is from dividing .2 by 88 .2272727 These numbers can be confirmed by using 1000 as the population, 120 as the smokers, 880 as the non smokers, 8 and 2 as the emphysema sufferers

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