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geometry

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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 -

    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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