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Math Help - Probability of finishing in first three places of a race

  1. #1
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    Probability of finishing in first three places of a race

    If we have a 10 runner horse race and we perceive the probabilities of winning the as follows...

    Horse 1 35%
    Horse 2 15%
    Horse 3 10%
    Horse 4 10%
    Horse 5 10%
    Horse 6 5%
    Horse 7 5%
    Horse 8 4%
    Horse 9 3%
    Horse 10 3%

    how would formulate the chance of a single horse finishing either first, second or third? Or would the probabilities of winning the race not be enough?

    p.s. I'm no maths expert so a dumbed down version would do if possible.

    Thanks,
    Adam.
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  2. #2
    MHF Contributor matheagle's Avatar
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    you need more info
    you really need to know the joint distribution of all 10, how they compete against each other.
    I've seen where in baseball team A can beat team B, while team B can dominate team C
    and yet C beats on A as well.
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