Number of contestants prize if tryout is held Income to a person if they stay at home Expected prize for a person Income of persons who did not tryout Total Income to the community 0 $0.00 $40,000 $0 $400,000 $400,000 1 $180,000.00 $40,000 $180,000 $360,000 $540,000 2 $190,000.00 $40,000 3 $205,000.00 $40,000 4 $225,000.00 $40,000 5 $250,000.00 $40,000 6 $270,000.00 $40,000 7 $285,000.00 $40,000 $405,000.00 8 $295,000.00 $40,000 $36,875.00 $375,000.00 9 $300,000.00 $40,000 $40,000 10 $302,000.00 $40,000 $30,200 $0 $302,000 Hint: Complete the table above. Assume: A person will try out if the expected prize >$40,000. Calculate the expected prize, complete the table and respond to the questions . How many persons will tryout? What is the total income of the community? To maximize total community income how many players should tryout? Explain why total income in part 2 is greater than the total income in part 1.
VD A national sports network offers a community a chance to join a pro team The winner of the tryouts takes home the prize but the others (losers) gain nothing. There are 10 persons in the village that could tryout. Each person will decide to join the game if the expected value of the game is higher than $40,000. This type of problem is often called “the winner takes all.” Hint: complete the table first.
Expected value of tryout = (Prize of the tryout) / (number of persons trying out) = expected prize
Income to the community = prize money + income of all persons who did not try out
|
Number of contestants |
prize if tryout is held |
Income to a person if they stay at home |
Expected prize for a person |
Income of persons who did not tryout |
Total Income to the community |
|
0 |
$0.00 |
$40,000 |
$0 |
$400,000 |
$400,000 |
|
1 |
$180,000.00 |
$40,000 |
$180,000 |
$360,000 |
$540,000 |
|
2 |
$190,000.00 |
$40,000 |
|||
|
3 |
$205,000.00 |
$40,000 |
|||
|
4 |
$225,000.00 |
$40,000 |
|||
|
5 |
$250,000.00 |
$40,000 |
|||
|
6 |
$270,000.00 |
$40,000 |
|||
|
7 |
$285,000.00 |
$40,000 |
$405,000.00 |
||
|
8 |
$295,000.00 |
$40,000 |
$36,875.00 |
$375,000.00 |
|
|
9 |
$300,000.00 |
$40,000 |
$40,000 |
||
|
10 |
$302,000.00 |
$40,000 |
$30,200 |
$0 |
$302,000 |
Hint: Complete the table above. Assume: A person will try out if the expected prize >$40,000.
Calculate the expected prize, complete the table and respond to the questions
.
- How many persons will tryout? What is the total income of the community?
- To maximize total community income how many players should tryout? Explain why total income in part 2 is greater than the total income in part 1.
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