Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to calculate cumulative chance from 2 different sources that are deciding on 1 result.

For example, there is a 1/4 chance from bonus and 1/10 chance in general. When we put those 2 together what do we get?

share|cite|improve this question
up vote 1 down vote accepted

It depends on whether the two 'chances' are independent. For example, suppose I know that there is a $1/2$ chance that it will rain tomorrow, a $1/2$ chance that it will snow tomorrow, and a $1/4$ chance that it will both rain and snow tomorrow. What is the probability that it will either rain or snow (or perhaps both) tomorrow?

If we simply add $1/2 + 1/2$, we are overcounting. Some of the chances that it will rain are tied to the chances that it will snow, as the probability of both happening is $1/4$. So we would say that the chance of rain or snow tomorrow is $1/2 + 1/2 - 1/4$.

This is analogous to the idea that maybe there are 2 boys in a chemistry class, 3 boys in an English class, and we happen to know that there is 1 boy in both. How many boys are in the chemistry and English classes? There are almost $2 + 3$, but we counted 1 boy twice. So there are $2 + 3 - 1$.

All together, this means that I don't know the exact answer to your question. It will be somewhere between $25\%$ and $35\%$. $%Any airplane fans out there? All together now...$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.