Posted by **angela** on Friday, June 8, 2012 at 7:01pm.

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.

- probability, not geometry -
**MathMate**, Friday, June 8, 2012 at 7:45pm
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

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