All 36 rolls of two dice on one grid and the 8 paths of three coins. Events are sets of outcomes — highlight them, then take unions, intersections and complements.

Knowing B happened shrinks the sample space to B. See it on the dice grid, then drag the splits of an area model and watch P(A | B) change.

A thousand people, a rare condition and a good test. Slide the base rate, sensitivity and false-positive rate and see why most positives are false alarms.

A distribution as bars on a beam. The expected value is where it balances, and the variance measures how far the weight sits from that point. Drag the bars.

Balls bounce left or right through a Galton board and pile up in bins. The pile takes the shape of C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ — change n and p and drop more.

Slide μ and σ, drag two points along the axis, and read off the area between them. The 68–95–99.7 rule and z-scores fall out of one curve.

Roll a die thousands of times and track the running average. It wanders at first, then settles on 3.5 inside a band that narrows like 1 / √n.

Draw samples from a lopsided distribution and average each one. The averages pile up into a bell curve whose width shrinks as σ / √n.

With only 23 people the chance of a shared birthday passes 50%. The exact curve against a seeded simulation, and the pairs that explain it.