Question

In: Statistics and Probability

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

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.

Perceived Risk
Smoking Status Very Harmful Somewhat Harmful Not Too Harmful Not at All Harmful
Current Smoker 58 35 5 1
Former Smoker 69 20 3 2
Never Smoked 85 11 2 1

(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.)

Solutions

Expert Solution

Total = 292

a) P(Former smoker) = 94/292 = 0.3219

b) P(very harmful) = 212/292 = 0.7260

c) P(very harmful | current smoker) = P(very harmful and current smoker)/P(current smoker)

                                                       = 58/99 = 0.5859

d) P(very harmful | former smoker) = P(very harmful and former smoker)/P(former smoker)

                                                       = 69/94 = 0.7340

e) P(very harmful | never smoked) = P(very harmful and never smoked)/P(never smoked)

                                                       = 85/99 = 0.8586

orchestra answered 2 years ago
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