## keebler01 4 years ago 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.

1. 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.

2. imranmeah91

^^ that makes much more sense

3. saifoo.khan

Thnks! :)

4. keebler01

thanks which one is correct!

5. mymomsaughter

how did you come up with the random numbers?

6. imranmeah91

why are you time traveling?