Ok, im taking a stats course right now and im trying to understand exactly how probability is defined. It says in the textbook that there are a few ways it can be defined. I understand the first one: Assume an experiment with n possible outcomes, each equally likely. If some event is satisfied by m of the n, then the probability of that event is m/n. However, if the events are not all equally likely, then this definition can't be used. There's also the other definitions like empirical probability and subjective probability, but these don't really give you a precise answer. Then there's the axiomatic probability with 4 axioms. But all it says is 1. P(A) >= 0, 2. P(S) = 1, 3. P(A U B) = P(A) + P(B) for mutually exclusive events A and B 4. P(the union of all mutually exclusive events) = sum from 1 to infinity (P(Ai)) this still doesnt give an explicit answer for what the probability of any event A would be! Using 3, to know P(A) i would need to know P(A U B) and P(B), and to know either of those i would need to know the other probabilities. I think the best definition is the first definition, but then there must be a way to reduce all elements of a sample space to being equally likely. Any insight would be greatly appreciated.