The Binomial Distribution

Successes in repeated trials

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Binomial: $P(X = k) = \binom nk p^k(1-p)^{n-k}$.
• Mean $np$, standard deviation $\sqrt{np(1 - p)}$.
• The chance of no successes is $(1-p)^n$: small risks add up.

Steps

1. n trials, probability p
2. Shapes of the binomial
3. Five heads out of ten
4. Into the tail
5. Is it binomial?
6. Defective parts