The table summarizes data on smoking status and perceived risk of smoking and is

Question

The table summarizes data on smoking status and perceived risk of smoking and is consistent with summary quantities obtained in a Gallup Poll conducted in November 2002. Assume that it is reasonable to consider these data as representative of the U.S. adult population.

(a) What is the probability that a randomly selected U.S. adult is a former smoker? (Give the answer to four decimals places.)


(b) What is the probability that a randomly selected U.S. adult views smoking as very harmful? (Give the answer to four decimals places.)


(c) What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a current smoker? (Give the answer to four decimals places.)


(d) What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a former smoker? (Give the answer to four decimals places.)


(e) What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual never smoked? (Give the answer to four decimals places.)


(f) How do the probabilities computed in Parts (c), (d), and (e) compare?

A. probabilities increase

B. probabilities decrease   

Perceived Risk Smoking Status Very Harmful Somewhat Harmful Not Too Harmful Not at All Harmful Current Smoker 55 27 5 1 Former Smoker 71 17 3 2 Never Smoked 94 8 2 1

Explanation / Answer

a)   probability that a randomly selected U.S. adult is a former smoker is 93 / 286 =0.3252

b)   probability that a randomly selected U.S. adult views smoking as very harmful is 220 / 286 =0.7692

(c) probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a current smoker is 55 / 220 =0.2500

(d) probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a former smoker is 71 / 220 =0.3227

Perceived Risk Smoking Status Very Harmful Somewhat Harmful Not Too Harmful Not at All Harmful Totals Current Smoker 55 27 5 1 88 Former Smoker 71 17 3 2 93 Never Smoked 94 8 2 1 105 Totals 220 52 10 4 286

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