Axioms of probability:
1. P(A) >= 0 for any event A. (probabilities are nonnegative.)
2. P(U) = 1. (probabilities of universe = 1. some outcome occurs every time you conduct the experiment.)
3. If A and B are mutually exclusive events, then P(A U B) = P(A) + P(B). (probability is additive over disjoint events.)
The other rules of probability can be proved from the axioms.
1. P() = 0. (the empty set has zero probability.)
2. P() = 1 - P(A). (the probability of a complement of an event.)
3. P(A U B) = P(A) + P(B) - P(A N B). (the addition rule of probability.)
