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View Diary: Morning feature: The Monty Hall problem (with poll and statistics questions answered) (310 comments)

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  •  Nope (3+ / 0-)
    Recommended by:
    Orinoco, Jimdotz, NCrissieB

    Being 50-1 against doesn't mean it WON'T happen, just that it's unlikely.  But there have been a lot of horse races!

    To show that the odds are wrong you'd have to look at a large set of races, the odds, and the winner.  I think the odds are pretty close to right, but not exactly.

    The reason not exactly is that these odds aren't really probabilities at all, they are proportions of the betting pool that bet a certain way.  

    •  Common problem in historical analysis. (3+ / 0-)
      Recommended by:
      terrypinder, plf515, winterbanyan

      "Event E happened."

      So what is the probability that Event E would happen?  Umm ... well ... uhh ... not zero.  We know it's not zero, because it did happen.  As for what its actual probability was, in most cases we neither know nor can know.

      What was the probability of Mine That Bird winning the Kentucky Derby?  Very close to 1.0 - barring injury or a jockey mistake - over the last 1/8 of a mile.  How about on the back stretch?  How about right before the bell rings and the announcer says "Annnnnd they're off?"

      We know what the betting odds were, and those reflect the best guesstimates of people who supposedly know something about horses and horse racing.  But we also knew what the betting odds were on an economic meltdown - the futures markets last summer - and those reflected the best guesstimates of people who supposedly know something about the economy.

      Oops.

      And OOPS.

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