Actually I understand the concept about the sum and product mentioned both by bishop and brilliant. I've studied them both in first year statistical and probability theory. I just mentioned them since they point to different concept even though both sources use the same name. So I guess my point is the term of sum and product rule of probability in Bishop's are not standard as I don't find them in other sources.
My question is :
Why is the format of the sum and product rule of probability (1.10 and 1.11) in Bishop book different than in other resources such as https://brilliant.org/wiki/probability-rule-of-sum/ and https://brilliant.org/wiki/probability-rule-of-product/ ?
I'm joining in.