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Suppose an individual is randomly selected from the population of all adult males living in the USA. Let $A$ be the event that the selected individual is over 6 $\mathrm{ft}$ 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?

P(A|B) > P(B|A)

Probability Topics

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all right, we're given to events here, a B in the event that a chosen individual has a height greater than six feet and be being the event that a chosen subject is a basketball player, and we're supposed compare these two probabilities and see which one is more likely to be greater. Now let's analyze the notation, see what these notations really say. So on the left hand side, we have probability of a given be meaning the probability that, given the subject is a basketball player, they are over six feet. In contrast, on the right hand side, we have the probability of be given a the probability that given that somebody is greater than six feet tall, that they are basketball player. Let's look at the left hand side first. Now, if we were to assemble all basketball players ever, we would expect most them to be on the taller side. Perhaps may be greater than six feet, however, if we look at the right hand side. If we collected every person who was six feet tall, not all of them, not as many of them, we would expect to be basketball players. Some of them might play a different sport, like volleyball or something like that, where some of them might just not play a sport at all. Therefore, we will probably expect this left hand probability be greater the probability that, given that somebody is a basketball player there greater than six feet, so thus the correct answer is left hand side.

University of California - Los Angeles

Probability Topics