Axioms of Probability

Probability · Axiom Academy

The mathematical foundation of probability theory: Kolmogorov's axioms The probability of any event is always a non-negative number. This axiom ensures that probabilities cannot be negative. Let's visualize what this means: The probability of the entire sample space (the certain event) is exactly 1. This ensures that one of the outcomes must occur. Watch how probabilities sum to 1: For mutually exclusive events (events that cannot occur simultaneously), the probability of their union equals the sum of their individual probabilities. Let's see this with rolling a die: 4. Derived Property: Complement Rule From the axioms, we can prove that the probability of an event not occurring equals 1 minus the probability that it does occur. This is one of the most useful derived properties:

This is the written version of the interactive lesson above. See the full Probability course.