How to Use a:b for Proportions & Fractions

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The discussion clarifies how to express probabilities using the a:b notation. A probability of 2/3 translates to a proportion of 2:3 when considering the ratio of successes to total events. However, if focusing on the ratio of successes to failures, the proportion changes to 2:1, representing the odds in favor. Additionally, the odds against the event occurring would be expressed as 1:2. Understanding these distinctions is crucial for accurately representing probabilities and proportions.
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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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