Home▸Board Games & Game Mathematics▸Sample Space, Events, and the Kolmogorov Axioms

🎲 Sample Space, Events, and the Kolmogorov Axioms

A 3D grid of the 36 outcomes of rolling two dice: pick events, combine them with union and intersection, and watch counted outcomes and probabilities update live against random rolls.

Board Games & Game Mathematics3DModerate60 FPS

The 6×6 grid of tiles is the full sample space Ω for rolling two dice — 36 equally likely ordered outcomes. Choosing events raises and colours the subsets of Ω that belong to them, turning abstract set theory into something you can count directly.

🔬 What It Demonstrates

Events are subsets of a sample space; probability is the fraction of Ω they cover. Union and intersection combine subsets, and the axioms — non-negativity, P(Ω)=1, and additivity over disjoint events — fall directly out of counting tiles.

🎮 How to Use

Pick Event A and Event B, then choose whether to view A alone, B alone, their union, or their intersection. Roll the dice (or enable auto-roll) to sample outcomes and watch the empirical frequency converge on the theoretical probability shown for the region.

💡 Did You Know?

Kolmogorov's three axioms — proposed in 1933 — are the entire foundation of modern probability theory. Every theorem, including Bayes' rule and the law of large numbers, is provable from just those three statements about sets.

⚙ Under the hood

A 3D grid of the 36 outcomes of rolling two dice: pick events, combine them with union and intersection, and watch counted outcomes and probabilities update live against random rolls.

diceprobabilityrandomnesseventsoutcomesmathematicsThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install