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Math Help - Odds vs Probability

  1. #1
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    Odds vs Probability

    A newspaper article preceeding the 1994 World Cup semifinal match between Italy and Bulgaria stated that "Itality is favored 10-11 to beat Bulgaria, which is rated at 10-3 to reach the final". Suppose this means that the odds that Italy wins are 11/10 and the odds that Bulgaria wins are 3/10. Find the probability that each team wins, and comment.

    Okay, so I know the transformation from Odds to Probability is given by:

    Probability = Odds / 1 + Odds

    and the transformation from Probabilities to Odds is given by:

    Odds = Probability / 1 - Probability


    Plugging in, I get:

    Probability Italy wins: 0.23

    Probability Bulgaria wins: 0.52

    Comment: So, from the question, it sounds like Bulgaria is less likely to win given the odds. However, if we calculate the probabilities, its clear that Bulgaria actually has a better shot at winning.


    Is this how you would approach the question? I found it a bit easy, I'm afraid I've missed something or interpreted it in a different way.

    Cheers
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  2. #2
    MHF Contributor
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    Hi GoodRobot,

    you've miscalculated...

    Italy at bookmaker odds of \frac{10}{11} is Odds_{win}=\frac{11}{10}\ \Rightarrow\ P_{win}=\frac{\frac{11}{10}}{\frac{11}{10}+\frac{1  0}{10}}=\frac{11}{11+10}=\frac{11}{21}

    Converting back...

    Odds_{win}=\frac{P}{1-P}=\frac{\frac{11}{21}}{\frac{21}{21}-\frac{11}{21}}

    Similarly for Bulgaria
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  3. #3
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    Ahh, I missed that.

    Thank you
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