geometry
posted by angela .
A community 5K run will award $ 50 to the winner. 40 people enter the race,and they each pay an entry fee of $20. Assuming thay are all equally likely to win, what is a fair price for
the competition? Round to the nearest
cent.

If they are all equally likely to win, the fair price is the expected value of the prize, namely
∑xP(x)
where
x=winning for a particular outcome,
P(x) is the probability of outcome x.
and the summation is summed over all possible outcomes.
The possible outcomes are:
$50 (winner), P($50)=1/40
$0 (others), P(0)=39/40
So the expected value is
∑50*(1/40)+0*(39/40)
=$1.25