Question 464896
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If they are all equally likely to win, a fair entry price would be the prize money divided by the number of entrants.  50 divided by 65, rounded to the nearest cent.


Here's another way to look at it.  Let's say that you wanted to be certain you would win the prize.  In order to be certain, you could buy all of the entries yourself.  In this case, if the prize were either less money or more money than the total amount you paid, then the entry fee would be unfair (either to you or to the race organizers).  The entry fee is fair only if the amount paid is exactly equal to the amount received.  In this case, if you bought all of the entries and the total amount paid is $50 (so that the amount paid equals the prize), then each of the 65 entries would cost 1/65th of the $50 you paid.


The fact that the entry fee is $20 per entrant is a red herring.  The information has nothing whatever to do with the answer to the question asked, because the question is to derive the fair price.  Had the question been: "Is the $20 entry fee a fair price?" the answer would be absolutely not since $1300 is a great deal more than $50.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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