Binomial Distribution

Binomial Distribution turns one of statistics' most important ideas into a clean, hands-on app: out of n trials, how many will succeed?

Whether you're a student meeting the topic for the first time, revising for an exam, or a teacher who needs a clear demo, this app keeps the focus on understanding — no clutter, no sign-up, no fuss.

WHAT YOU CAN DO

- Concept — A plain-language explanation of the binomial distribution, its probability mass function, mean, and variance, plus how it connects to Bernoulli trials and the normal approximation, with formulas rendered cleanly.

- Calculator — Set the number of trials n, the success probability p, and a count k, then instantly see P(X = k), P(X ≤ k), P(X > k), the mean, variance, and standard deviation.

- Chart — Visualize the shape of the distribution. Switch between the PMF and CDF and change n and p to watch the bars shift, peak near the mean, and turn symmetric when p = 0.5.

- Simulation — Run a single n-trial experiment and count the successes, or run hundreds at once and watch the histogram build while the average closes in on the theoretical value np (the law of large numbers in action).

- Examples — Three worked, real-world problems — coin flips, factory quality control, and multiple-choice guessing — that show exactly when and how to apply the formula.

WHY THIS DISTRIBUTION MATTERS

The binomial distribution answers questions like "How many will succeed out of a fixed number of attempts?" It appears in quality control, A/B testing, polling, genetics, gaming, and any situation built from repeated independent yes/no trials with a constant chance of success.

Convention used: X is the number of successes in n trials, with k = 0, 1, 2, …, n
P(X = k) = C(n, k) · p^k · (1 − p)^(n − k)
Mean = np Variance = np(1 − p)

BUILT TO BE SIMPLE
- Lightweight and fast.
- Clear, distraction-free interface.
- Interactive sliders, steppers, and live results — learn by doing.

Note: an internet connection is used to display the formulas and ads.

Master the binomial distribution by seeing it, computing it, and simulating it — all in one place.