Question 1076925: Eight hundred chances are sold at $6 apiece for a raffle. There is a grand prize of $700, two second prizes of $300, and five third prizes of $100. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
Answer by alanc(27)   (Show Source):
You can put this solution on YOUR website! Eight hundred chances are sold at $6 apiece for a raffle. There is a grand prize of $700, two second prizes of $300, and five third prizes of $100. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
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let the variable be x : = Dollar Prize outcome of a ticket.
E[x] = $700*(1/800) + $300*(2/800) + $100 * (5/800)
E[x] = (700 + 600 + 500)/800 = 1800 / 800 = $2.25
Your expected prize value from a ticket is $2.25
This is NOT a fair game because the expected value of the lottery is $2.25, which is lower than the cost of buying a ticket at $6 .
If the price for playing the game was less than or equal to $2.25, then the game would be fair.
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