I have always wondered: Is the product rule and addition rule for that matter axioms of the probability theory or can they actually be proven from more general principles? The reason I ask is, and it might be a bit silly, that I have always thought I missed out on something in probability theory. As an example: Consider tossing two coins. You can get: tails heads, heads tails, tails tails, heads heads Then by the product rule the chance of each of these out comes is 1/4, and their sum adds up to 1 as it should. But I came to think: Why is it that it necessarily adds up to 1? So I thought thats simply the binomial theorem, so you can sort of say that the binomial theorem fits nicely with the way we "count" different outcomes. But what if it had not? What is it that assures that no matter what the rules for calculating probability of events will preserve the fact that Ʃp=1? Maybe this is gibberish to you, but if you can help me understand any of this just a little better, I'd be glad.