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Probability Basics / Probability Axioms
Probability Axioms
Section 1 of 3: Kolmogorov's Axioms

The modern theory of probability is based on three axioms formulated by Andrey Kolmogorov in 1933. These axioms provide a mathematical foundation for probability theory.

Axiom 1: Non-negativity

For any event A, the probability of A is non-negative:

P(A) ≥ 0

Axiom 2: Normalization

The probability of the entire sample space Ω is 1:

P(Ω) = 1

Axiom 3: Countable Additivity

For a countable sequence of mutually exclusive events A₁, A₂, A₃, ..., the probability of their union is the sum of their individual probabilities:

P(A₁ ∪ A₂ ∪ A₃ ∪ ...) = P(A₁) + P(A₂) + P(A₃) + ...