in reply to What are "the odds"?
in thread Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)?

In the example you gave the odds are 3:1 (or 3, if one follows the common practice viewing this as a ratio), but decidedly not 25%. Granted, in colloquial speech, "odds" and "probability" are often used interchangeably, but technically odds and probabilities are "interchangeable" only in the limited sense that one can derive one from the other. They mean different things. See here.

Update: In response to chas's comment, I replaced the link to MathWorld's definition (which was, indeed, well, odd) with a link to a clearer explanation of odds vs. probabilities.

the lowliest monk

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Re^2: What are "the odds"?
by chas (Priest) on Jun 14, 2005 at 12:28 UTC
    By the way, I consider that the definition of "odds of winning" on that Mathworld page is badly stated since that expression is exactly what almost every mathematician in the world would call "odds against winning." I have to think that whoever wrote it was just confused.