An interactive visualization that makes Bayes' theorem something you can actually see
burny_tech · x · 2026-11-12
@matheorems shares a visual, interactive take on Bayes' theorem: a probability is a share of dots in a box. P(A) is the area covered by circle A, and P(B|A) is the lens-shaped overlap of A and B divided by A.
Sliding the circles updates every number live — apart, the lens is empty and both conditionals are 0; tuck B inside A and P(A|B) becomes 1. Since the lens is the same region in both directions, P(B|A)·P(A) = P(A|B)·P(B) falls out visually, and dividing gives Bayes' theorem. A formula box recomputes each side live and always matches the picture.
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