Probability Theory

Probability

Probability Axioms -- Probability Distributions

The basic theorems of probability can be developed easily from the Probability Axioms and Set Theory.

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, is given by the sum of the probabilities for all 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, , is given by the sum of the probabilities of the two events minus the probability of both.

The formulae below express the same ideas in algebraic terms.

1. SUM Pr[E_i] = 1
2. Pr[A₁*A₂] = SUM of Pr[E_i] for all E_i in both A₁ and A₂.
3. Pr[A₁+A₂] = Pr[A₁] + Pr[A₂] - Pr[A₁*A₂]

(in these equations, "+" means "or" and "*" means "and")

The probability of some event happening knowing that another event happened before can be computed using Conditional Probability.