Question

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)?.

Answer 1

Answer:

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)