I mean, is there a mathematical argument or best said, relationship, to another field of math, the nature of adding or multiplicating two probabilities? Like, could we think that we add things, imagining we didn't "reason" or made it intuitively because they are exclusive? I know this may seem senseless because two exclusive quantities, as far as I get it, wouldn't add at all (I imagined water and oil; also if I got stupid ideas or I'm confusing things, let me know, please)
Sorry if this question is dumb, I have only taken one class of probability and stats and it was more of the applications of these topics rather than discussing them. It would be cool if y'all also could recommend me a book about "math discussion" for newbies or ideas to develop a more mature appreciation of math topics, rather than only getting the idea and knowing how to use the concept as we do in class. I recently started rediscovering how fantastic maths and logic are after reading a couple of discussions here.
Thanks for anyone who spends his time answering!