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To: M. Frank Greiffenstein who wrote (587)	12/11/2000 10:17:25 PM
From: Bilow	Respond to of 24758

Hi M. Frank Greiffenstein; Yes, I agree that the definition is a limited one. The generalization is obvious, and would still be a ratio of probabilities. Wouldn't you agree? But in fact, for the vast majority of cases, the dictionary calculation is the correct one. I'll post some links showing this in a minute... I gave an example of the generalization, and I'll repeat it here: As an example, consider the odds of throwing a "1" with a die before getting any "even" roll. We will all (hopefully) agree that the odds of this are 3 to 1 against, as there are three "even" faces, and only one "1" face. Compare this to the ratio of the probabilities. The probability of rolling a "1" is 1/6. The probability of rolling an "even" is 3/6 = 1/2. The ratio of the probabilities is 1/2 to 1/6, or 3 to 1. As we both agree, the odds are the ratio of the probabilities. By the way, this example also illustrates your point about "not necessarily exhaustive" occurrences. #reply-14997072 In any case, for the purpose of computing the odds that Clarke wrote about, exhaustion of occurrences is implied... -- Carl