Two finalists are in a tennis match with the winner to recei

Two finalists are in a tennis match with the winner to receive $40,000 and the loser $25,000. A) What are the two players mathematical expectations if they are equally matched? B) What are the two players mathematical expectations if their probabilities of winning are 2/3 and 1/3?

Solution

(a)

Since player are equally matched so both have probability of winning 0.5. Mathematical expectattion of winning is

(0.5) * ($40,000) + (0.5) * ($25,000) = $32,500

In this case mathematical expectation of both player is same and it is equal to $32,500.

(b)

Mathematical expectation for the player with winning probability 2/3:

(2/3) * ($40,000) + (1-(2/3)) * ($25,000) = $35,000

Mathematical expectation for the player with winning probability 1/3:

(1/3) * ($40,000) + (1-(1/3)) * ($25,000) = $30,000