The winner of a tennis tournament earns $50,000 and the runner-up earns $25,000.

Question

The winner of a tennis tournament earns $50,000 and the runner-up earns $25,000. What are the expected earnings of each of the two finalists if (a) they are evenly matched? (b) their probabilities of winning are 0.65 and 0.35? (c) their probabilities of winning are 0.80 and 0.20? [Note: you will need to calculate two expected values in each case, one for the favored player and one for the undedog]

***All parameters must be calculated from scratch using the appropriate probability distribution. Do not use short-cut formulas such as the ones for the mean and variance of a binomial distribution.All probabilities must be calculated from first principles, as in the first homework assignment. DO NOT use short-cut formulas, such as the binomial equation.

Explanation / Answer

let A and B are two players

a) if both have same probabilty of winning or losing ; their expected earning =(1/2)*50000+(1/2)*25000=37500

b) for given probability; expected earning of A =0.65*50000+0.35*25000=41250

and expected earning of B=0.35*50000+0.65*25000=33750

c) expected earning of A==0.8*50000+0.2*25000=45000

expected earning of B==0.2*50000+0.8*25000=30000

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