anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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saifoo.khan
  • saifoo.khan
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. ----- Find expected value. P(win) = 1/55 P(lose) = 54/55 --- Random winning #'s: 30,-20 ----- E(x) = (1/55)(30)+(54/55)(-20) = (30-54*20)/55 = -1050/55 --- = -$19.09 =============== All the competitors are contributing $19.09 to the organizers. =============== For a fair price the price to compete should be $x. The Random winnings would be 50-x, -x --- Expected winnings would be zero. E(x) = (1/55)(50-x)+(54/55)(-x) = 0 --- [50-x-54x)/55 = 0 -55x+50 = 0 x = 50/55 x = $0.91 Each runner should pay 91 cents to compete.
anonymous
  • anonymous
^^ that makes much more sense
saifoo.khan
  • saifoo.khan
Thnks! :)

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anonymous
  • anonymous
thanks which one is correct!
anonymous
  • anonymous
how did you come up with the random numbers?
anonymous
  • anonymous
why are you time traveling?

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