A community 5K run will award $50 to the winner. 60 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
Can anyone help me get started on this one?
Random-gain values: 50-20 = 30 ; -20
Probabilities: 1/60 ; 59/60
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E(gain)= 30(1/60)-20(59/60) = 1/2 - (59/3)= (3-59)/6 = -$9.33
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A fair price would be 20-9.33 = $10.67
To determine the fair price for the competition, we need to consider the total cost of the entry fees paid by the participants and the prize money awarded to the winner.
First, we need to calculate the total amount collected from the entry fees. Since there are 60 participants, and each participant pays an entry fee of $20, the total amount collected would be:
Total Entry Fees = Number of Participants * Entry Fee
Total Entry Fees = 60 * $20 = $1200
Next, we consider the prize money of $50 given to the winner. Since all participants are equally likely to win, each participant has a 1 in 60 chance of winning.
Now, let's calculate how much money should be awarded to each participant if the competition is fair. We take the total amount collected from entry fees and divide it equally among all participants:
Fair Share = Total Entry Fees / Number of Participants
Fair Share = $1200 / 60 = $20
Therefore, a fair price for the competition would be $20.