Question 405479: . Essay; show all work. A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.
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Find expected value.
P(win) = 1/55
P(lose) = 54/55
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Random winning #'s: 30,-20
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E(x) = (1/55)(30)+(54/55)(-20)
= (30-54*20)/55 = -1050/55
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= -$19.09
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All the competitors are contributing
$19.09 to the organizers.
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For a fair price the price to compete should be $x.
The Random winnings would be 50-x, -x
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Expected winnings would be zero.
E(x) = (1/55)(50-x)+(54/55)(-x) = 0
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[50-x-54x)/55 = 0
-55x+50 = 0
x = 50/55
x = $0.91
Each runner should pay 91 cents to compete.
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Cheers,
Stan H.
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