How to Use a:b for Proportions & Fractions

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SUMMARY

The discussion clarifies the distinction between probability and proportions, specifically in the context of expressing probabilities using the notation a:b. A probability of 2/3 translates to a proportion of 2:3 when considering the ratio of successes to total events. Conversely, when evaluating the proportion of successes to failures, the odds are represented as 2:1, with the odds against being 1:2. This nuanced understanding is crucial for accurately conveying statistical information.

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quasar987
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It has something to do about proportion and fractions. But say I want to express in that notation the fact that some event happens with a probability 2/3. Does that write 2:3 or 2:1 or something else?
 
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A probability is not directly a proportion. If you are talking about the "proportion of 'successes' to all events", then probability 2/3 is 2:3. But if your proportion is "proportion of 'successes' to 'failures'" then the proportion is 2:1 (odds in favor). You could also say, by the way, that the "odds against" are 1:2.
 

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