Suppose that in a certain population, 28% of adults are regular smokers. Of the
ID: 2921731 • Letter: S
Question
Suppose that in a certain population, 28% of adults are regular smokers. Of the smokers, 15.8% develop emphysema, while of the nonsmokers, 0 9% develop emphysema. An adult from this population is randomly chosen. a) Find the probability that this person is a smoker, given that the person develops emphysema b) Find the probability that this person is not a smoker, given that the person does not develop emphysema a) The probability that this person is a smoker, given that the person develops emphysema, is 11 (Do not round until the final answer. Then round to four decimal places as needed.) IS b) The probability that this person is not a smoker, given that the person does not develop emphysema, is Do not round until the final answer. Then round to four decimal places as needed.)Explanation / Answer
P(smokers) = 0.28
P(non-smokers) = 1 - 0.28 = 0.72
P(emphysema | smokers) = 0.158
P(emphysema | non-smokers) = 0.009
a) P(emphysema) = P(emphysema | smokers) * P(smokers) + P(emphysema | non-smokers) * P(non-smokers)
= 0.158 * 0.28 + 0.009 * 0.72
= 0.05072
P(smoker | emphysema) = P(emphysema | smokers) * P(smokers) / P(emphysema)
= 0.158 * 0.28 / 0.05072
= 0.8722
b) P(not emphysema) = 1 - 0.05072 = 0.94928
P(not emphysema | non-smokers) = 1 - P(emphysema | non-smokers) = 1 - 0.158 = 0.842
P(non-smoker | not emphysema) = P(not emphysema | non-smokers) * P(non-smokers) / P(not emphysema)
= 0.842 * 0.72 / 0.94928
= 0.6386
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