SOLUTION: Debra is buying prizes for a game at her school�s fundraiser. The game has three levels of prizes (and some players will lose), and she has already bought the second and third pri

Question 130135: Debra is buying prizes for a game at her school�s fundraiser. The game has three levels of prizes (and some players will lose), and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game�s manufacturer has supplied her with the probabilities of winning first, second and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize?
Prize Cost of Prize Probability
1st ? 0.15
2nd $1.25 0.30
3rd $0.75 0.45

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Debra is buying prizes for a game at her school�s fundraiser. The game has three levels of prizes (and some players will lose), and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game�s manufacturer has supplied her with the probabilities of winning first, second and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize?
Prize Cost of Prize Probability
1st ? 0.15
2nd $1.25 0.30
3rd $0.75 0.45
-------------------
Let the 1st prize value be "x" dollars.
For the fundraiser to gain $1 on each ticket the expected "gain" for
the ticket purchaser must be -1 dollar.
--------------------------------
Since the winning probabilities add to 0.9, the prob of losing $3 is 0.1
---------------------------------
EQUATION:
E(x) = 0.15x + 0.3*1.25+0.45*0.75-3*0.1 = -1
0.15x + 0.4125 = -1
0.15x = -1.4125
x = -9.42
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The 1st prize should be $9.42
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Cheers,
Stan H.
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