The winner of a tennis tournament gets $40,000 and the runner-up gets $15,000. What are the two finalists’ mathematical expectations if

Question

a. they are evenly matched?

b. their probabilities of winning are 0.65 and 0.35?

Answer 1

a. equally matched, Expected Value or Expected winnings = 1/2 x 40K + 1/2 15K = 20K+7.5K = $27,500

That's just the average of 40K and 15K. K=$1000. (40+15)/2=27.5 is the mean

b. If one's probability is 0.65 then Expected Value = 0.65(40K) +K 0.35(15K) = 26k+5.25K = $31,250

and the other's Expected Value is 0.35(40K) + 0.65(15K) = 23.75K = $23,750

That's a weighted average. The average weighted by their probabilities.

The expected winnings for both will sum to the sum of $40,000 + $15,000 = $55,000.

$31,250 + $23,750 = $55,000