ProbabilityTheory

ProbabilityAndStatistics

ProbabilityAxioms -- ProbabilityDistributions

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

1. The sum of the probabilities for all the elementary events is one.
2. 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.
3. 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}