The basic theorems of probability can be developed easily from the ProbabilityAxioms and SetTheory.

- The sum of the probabilities for all the
*elementary events*is one. - For any arbitrary events, A1 and A2, the probability of both events, Pr{A1*A2}, is given by the sum of the probabilities of the
*elementary events*in both A1 and A2. If the intersection is empty, then the probability is exactly zero. - For any arbitrary events, A1 and A2, the probability of either or both, Pr{A1+A2}, is given by Pr{A1}+Pr{A2}-Pr{A1*A2}

[RABeldin ]