Duyệt các ví dụ hoạt ảnh Probability được tuyển chọn trong Math, bao gồm các cảnh Manim có thể tái sử dụng, chứng minh trực quan và ý tưởng sẵn sàng để giảng dạy.
Math · 3 hoạt ảnh
This animation contrasts permutations (order matters) with combinations (order doesn't matter) using a concrete example of choosing 2 items from {A, B, C}. A tree diagram visually enumerates all 6 permutations, then groups are collapsed to show only 3 combinations, making the divide-by-r! factor intuitive.
Demonstrates the Central Limit Theorem by starting with a non-normal (uniform) population, then repeatedly drawing samples of size n=30 and computing their means. As more sample means are collected, the histogram of means converges to a bell curve regardless of the original distribution's shape.
Introduces three fundamental probability distributions — Normal, Binomial, and Poisson — with visual representations and key formulas. For the Normal distribution, the 68-95-99.7 empirical rule is animated by progressively shading regions under the bell curve.
