Show COMPLETE solution using probability rules. Please explain The winner of a t
ID: 3207120 • Letter: S
Question
Show COMPLETE solution using probability rules. Please explain 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? ***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 X= favored player
Y= undedog player
a)
evenly matched means probability of winning or lossing=0.5 for both
earning of X = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.5*50000) + (0.5*25000)
= 37500
Expected earning of favered player X is $37,500.
earning of Y = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.5*50000) + (0.5*25000)
= 37500
Expected earning of undedog player Y is $37,500.
b)
Probability of winning X=0.65
Probability of Lossing X=1-0.65=0.35
Probability of winning Y=0.35
Probability of Lossing X=1-0.35=0.65
earning of X = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.65*50000) + (0.35*25000)
= 41250
Expected earning of favered player X is $41,250.
earning of Y = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.35*50000) + (0.65*25000)
= 33750
Expected earning of undedog player Y is $33,750.
c)
Probability of winning X=0.80
Probability of Lossing X=1-0.80=0.20
Probability of winning Y=0.20
Probability of Lossing X=1-0.20=0.80
earning of X = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.80*50000) + (0.20*25000)
= 45000
Expected earning of favered player X is $45,000.
earning of Y = probability of winning * winning amount + probability of lossing * lossing amount
=( 0.20*50000) + (0.80*25000)
= 30000
Expected earning of undedog player Y is $30,000.