SEOULTRA
Probability & Statistics
Set the board size yourself, run the drop, and compare the noisy histogram with the exact Pascal coefficients revealed in the same view.
Change the setup, run the experiment, and reveal the exact combinatorics without switching themes or camera angles.
Landing bins always equal bounce rows + 1, so editing either field keeps the board mathematically consistent.
A Galton board is a simple machine that drops balls through rows of pegs. Every time a ball hits a peg, it bounces left or right.
When many balls fall, most land near the middle and only a few reach the far edges. That makes the familiar bell-shaped pattern you see at the bottom.
If each bounce is equally likely to go left or right, then a ball experiences a sequence of independent Bernoulli trials. After n rows, the probability of ending in bin k is:
Here C(n, k) counts how many distinct left-right paths lead to that landing bin. With 8 rows there are 28 = 256 possible paths, and each bin gets a share based on its coefficient.
Pascal's triangle is a number pattern. It starts with 1 at the top, and each new number is made by adding the two numbers above it.
On this board, row 8 is 1, 8, 28, 56, 70, 56, 28, 8, 1. Those numbers tell you how many different paths can end in each of the 9 landing bins after 8 bounces.
One run can look a little messy because you only dropped a limited number of balls. If you run it again and again, the bars will settle into a smoother middle-heavy shape. The reveal helps you compare the random result with the exact path counts underneath.