Question 145174This question is from textbook
: I am having trouble trying to figure out how to solve this problem of Expected Value. Could anyone please help me with this? Thank you so much!
A charitable organization is raffling a car worth $20,000 to raise money and needs to decide which of the following scenarios would be the most profitable based on expected value of the proposed game.
Case A: 150 tickets are sold at $200.00 each.
Case B: 75 tickets are sold at $500 each.
1. Determine the expected value for the winnings of the players in Case A.
2. Determine the expected value for the winnings of the players in Case B.
3. Based on the expected values, which game would potentially raise more for the organization? Why? Are there any factors other than expected value that should be considered in this decision?
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A charitable organization is raffling a car worth $20,000 to raise money and needs to decide which of the following scenarios would be the most profitable based on expected value of the proposed game.
Case A: 150 tickets are sold at $200.00 each.
Case B: 75 tickets are sold at $500 each.
1. Determine the expected value for the winnings of the players in Case A.
Random variable values for "gain" are 20,000 and -200
Corresonding probabilitites are 1/150 and 149/150
E(X) = 20,000(1/150) + (-200)(149/150) = -$65.33
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2. Determine the expected value for the winnings of the players in Case B.
X values: 20,000 and -500
P(X) values: 1/75 and 74/75
E(X) = 20,000(1/75) + (-500)(74/75) = -$266.67
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3. Based on the expected values, which game would potentially raise more for the organization? Why?
Plan B because the greater expected loss for the player assures that
the organization has a higher expected gain.
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Are there any factors other than expected value that should be considered in this decision?
I'll leave that to you. You might consider the risk involved in trying to
market $500 tickets compared to the risk of selling $200 tickets.
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Cheers,
Stan H.
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