In a region, 12.065% of the adult population are smokers, 0.932% are smokers wit

Question

In a region, 12.065% of the adult population are smokers, 0.932% are smokers with emphysema, and 0.275% are non-smokers with emphysema.
(a) What is the probability that a person, selected at random, has emphysema?
(b) Given that a 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?
(d) Given a person has emphysema, what is the probability that this person is a
non-smoker?
(e) Given your answers to the questions above, does your data support the notion
that getting emphysema is statistically independent of smoking?
Hint: Let E be the event of a person having emphysema and D the event that a
person does not have emphysema. Similarly, let S denote the event that a person is
a smoker and N for a non-smoker.

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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