Suppose an individual is randomly selected from the populati

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(AuB) or P(BuA)? Explain Why?

Solution

You probem shows P(AuB) and P(BuA). That is union of A and B. By the commutaitive property, both are same.

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I think you want to ask: Which do you think is larger, P(A | B) or P(B | A)?

P(A | B) shows the event that the selected individual is over 6 ft given that it is a professional basketball player.

P(B | A) shows the event that the selected individual is a professional basketball player given that it is over 6 ft.

P(A | B) should be larger because generally basket ball player has good height .