Question

The winner of a tournament earns $50,000 and the runner-up earns $25,000. What are the expected earnings of a person playing in the finals if her probability of winning is:

            (a)        0.50 ?

            (b)       0.65 ?

            (c)        0.80 ?

*Show all appropriate steps and formulas/equations used

Answer 1

The expected value of a random variable is obtained by taking the sum of the products of the random variate taking values with there respective probabilities.

Total prize money is $50000 + $25000 = $75000

a) Probability = 0.50

The expected earning of winner is $75000*0.50 = $37500

The expected earning of runner is $75000*0.50 = $37500

b) Probability = 0.65

The expected earning of winner is $75000*0.65 = $487500

The expected earning of runner is $75000*0.35 = $26250

c)

Probability = 0.80

The expected earning of a winner is $75000*0.80 = $60000

The expected earning of a runner is $75000*0.20 = $15000