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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.