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 is larger, P (A|B) or P (B|A) ?.

P (A|B)

P (A|B) is expected to be bigger because most basketball players are over 6ft but only a few tall people (6ft + ) are basketball players.

Step-by-step explanation:

P (A|B) means probability that the selected individual is over 6 ft given that he plays basketball

P (B|A) means the probability that the selected individual plays basketball, given that he is over 6ft.

P (A|B) is expected to be bigger because most basketball players are over 6ft but only a few tall people (6ft + ) are basketball players.

P (A) = Probability that the selected individual is over 6 ft in height; normally in a total population of humans, this would be a very small figure, (there are way more people 6ft and under in the world than there are people taller than 6ft)

P (A) is approximated to be 0.05

P (B) is the probability that the selected individual is a professional basketball player. It is even rarer to get a professional basketball player when all the population is considered. P (B) is approximated to be 0.0005

Mathematically,

P (A|B) = P (A n B) / P (B)

P (B|A) = P (A n B) / P (A)

P (A|B) = P (A n B) / 0.0005 = 2000 * P (A n B)

P (B|A) = P (A n B) / 0.05 = 20 * P (A n B)

Since P (A n B) is equal for the two cases, P (A|B) > P (B|A)