The table at the top of the next page 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 adult American population.
a. What is the probability that a randomly selected adult American is a former smoker?
b. What is the probability that a randomly selected adult American views smoking as very harmful?
c. What is the probability that a randomly selected adult American views smoking as very harmful given that the selected individual is a current smoker?
d. What is the probability that a randomly selected adult American views smoking as very harmful given that the selected individual is a former smoker?
e. What is the probability that a randomly selected adult American views smoking as very harmful given that the selected individual never smoked?
f. How do the probabilities computed in Parts (c), (d), and (e) compare? Does this surprise you? Explain.