Rolling two dice has a sample space Ω of 36 equally likely ordered outcomes (i, j), each with probability 1/36. The 6×6 grid in the scene is Ω — one raised tile per outcome. An event is just a subset of Ω, like "the sum is 7" or "at least one die shows 6." Selecting an event colours and raises the tiles that belong to it; the fraction of Ω it covers is its probability.
Andrey Kolmogorov's 1933 axiomatisation reduced all of probability theory to just three rules on subsets of a sample space — non-negativity, total probability one, and additivity over disjoint events. Everything else, including Bayes' theorem and the law of large numbers, follows from those three statements.
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.
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.
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.
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.