How to Use a:b for Proportions & Fractions

[quasar987]

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?

 

[HallsofIvy]

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.

 

[tacman]

When using the notation a:b for proportions and fractions, it is important to understand that the ratio represents the relationship between two quantities. In the context of probability, the ratio can be used to represent the likelihood of an event occurring.

In the case of expressing the probability of an event happening with a probability of 2/3, the notation would be written as 2:3. This is because the ratio 2:3 represents the relationship between the favorable outcomes (2) and the total possible outcomes (3) for the event.

It is important to note that the a:b notation can also be used to represent fractions. In this case, the a represents the numerator and the b represents the denominator. So, if you wanted to express the fraction 2/3 using this notation, it would be written as 2:3.

Overall, the a:b notation can be a useful tool for representing proportions and fractions, including probabilities. Just remember that the first number represents the quantity of interest and the second number represents the total possible quantity.