SOLUTION: Essay. Show all work. A community 5k run will award $50 to the winner. 50 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win,
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Question 443025: Essay. Show all work. A community 5k run will award $50 to the winner. 50 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. 50 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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Random gain values for the runners assuming they pay "x" to compete:
-x and 50-x
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Corresponding probabilities:
(49/50) and (1/50)
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E(x) = (49/50)(-x)+(1/50)(50-x)
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For the entry price to be "fair" E(x) must be zero.
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Solve:
(49/50)(-x)+(1/50)(50-x)
[-49x+50-x]/50 = 0
-50x+50 = 0
x = $1.00
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Cheers,
Stan H.
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