Question 488402: essay show all work, a community 5k run will award $50 to the winner, 35 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.
thank you ahead of time for your help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! essay show all work, a community 5k run will award $50 to the winner, 35 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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Probability of winning: 1/35
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Let cost to participate be "x".
Random winnings: 50-x ; -x
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Expected winnings = (1/35)(50-x) + (34/35)(-x)
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A fair price means the expected winnings is zero.
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Solve: (1/35)(50-x) + (34/35)(-x) = 0
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Multiply thru by 35 to get:
50-x -35x = 0
36x = 50
x = $1.39 (that is the "fair" price for entering the race)
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Cheers,
Stan H.
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