Suppose an individual is randomly selected from the population of all adult males living in the United States. Let ?A ?be the event that the selected individual is over 6 ft in height, and let ?B ?be the event that the selected individual is a professional basketball player. Which do you think is larger, P(A|B) or P(B|A) ? Why?

Problem 46E Answer: Step1: We have suppose an individual is randomly selected from the population of all adult males living in the United States. Let A be the event that the selected individual is over 6 ft in height, and let B be the event that the selected individual is a professional basketball player. Our goal is to check whether P(A|B) larger or P(B|A) larger and Why Step2: P(A/B) = Probability that a person is over 6 ft in height, knowing that he is a basketball player P(B/A) = Probability that a person is a basketball player, knowing that he is over 6 ft in height “P(A/B) is much larger than P(B/A)” because, almost all basketball players are tall. So the proba-bility that a random basketball player is over 6 ft in height is high. P(B/A) is small, because only a very small percentage of US adult males are professional basketball player. In other words, the the number of individuals who are professional basketball players is very small compared to the number of male adults over 6 ft in height.