The binomial distribution: heads in n coin flips
Bar charts show P(k) = C(n,k)/2^n for n = 1, 2, 3, 4, 6, 8, and 10, with heights generated directly from Pascal's triangle. As n grows, the discrete bars smooth into the familiar bell-shaped normal curve, making the Central Limit Theorem visible rather than abstract. Useful for students and teachers connecting combinatorics, probability, and statistics, this version fixes a transition glitch where leftover numbers briefly floated onscreen before the n=8 chart appeared.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Apply ALL of the following review notes precisely; keep everything else identical. This video is for social media and must be impeccable. - Excellent animations, only detail to correct is some floating numbers from before appear in the transition to n=8
Make the next one in this series
- Overlay the normal curve equation and shade the area matching each bar chart's total probability
- Animate the same convergence using a Galton board with balls falling into bins
- Show how the mean and variance formulas np and np(1-p) predict the curve's center and spread
