High School Multiply Probabilities vs. Sum of the Squares

[jaydnul]

Hi! I'm getting confused by these two things. If I have two uncorrelated probabilistic events, and I want to know the probability of seeing them both land beyond 3.3 sigma (for example), do I multiply the probabilities .001*.001 or do I do sum of the squares sqrt(.001^2 + .001^2). I assume it is the former, but can you explain what context we would use sum of the squares instead?

 

[Dale]

If I have two uncorrelated probabilistic events, and I want to know the probability of seeing them both land beyond 3.3 sigma (for example), do I multiply the probabilities .001*.001 or do I do sum of the squares sqrt(.001^2 + .001^2).

Uncorrelated and independent are different things. If they are independent then you multiply the probabilities. Correlation is simply one specific type of dependence. However, it is easy to come up with examples where one event causes the other with 100% certainty (so the probability of seeing them both is equal to the probability of the cause) and yet they are uncorrelated.

explain what context we would use sum of the squares instead?

I don't know of a context where you use the sum of the squares of the probabilities. That could easily lead to a number greater than 1, which couldn’t be a probability.

Often you use the sum of the squares of the standard deviations. For example, to calculate the variance of the sum of two random variables.

 

[jaydnul]

Ok thanks that makes sense!