The binomial, by hand

Drop balls through a board of pegs. Change the rows and the bias of the coin and watch the pile follow the binomial distribution.

Probability machine

Rows of pegs

There is one more bin than rows.

Balls

Chance of bouncing right

0.50

This run

Mean bin: -
Expected n p: 5.00
Largest bin: -

What you are looking at

Each ball meets one peg per row and goes right with probability p. After n rows, the number of rights k decides the bin, so the bins count draws from a binomial distribution:

P(k) = \binom{n}{k} p^{k} (1-p)^{n-k}

(1)

The mean bin is n p. With more balls the pile looks more like the formula; with more rows and a fair coin it starts to look like a normal curve.