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You may also think of these axioms as "truths" upon which we base all the mathematical derivations related to probability.

Axiom 1: P(E) ³ 0 for any event E. This just says that we start by defining probability to be nonnegative. Note that P(E)=0 indicates that the event will definitely not happen.

Axiom 2: P(S) = 1. Since S is the set of all possible outcomes for an experiment, the event S must by definition occur, i.e., at least one of the outcomes in S will definitely occur and we assign a probability of 1 to this event.

Axiom 3: For any finite (or countably infinite) collection of mutually exclusive events {E₁,E₂,...}, P(E₁È E₂È E₃È ...) = P(E₁)+P(E₂)+P(E₃) +... This axiom thus says that the probability that at least one of the mutually exclusive events E₁,E₂,... happens is the sum of the individual probabilities of each event.