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Binomial Probability Calculator

Compute the probability of k successes in n binomial trials.

Introduction

Binomial Probability Calculator — Compute the probability of k successes in n binomial trials. Enter Trials (n), Successes (k), Success probability (p) to get an instant, accurate result.

Formula

Binomial PMF: P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ, the probability of exactly k successes in n independent trials with success probability p.

Step-by-step

  1. Enter the Trials (n).
  2. Enter the Successes (k).
  3. Enter the Success probability (p).
  4. Click Calculate to see your result instantly.

Real-world example

Example: With Trials (n) = 10, Successes (k) = 3, Success probability (p) = 0.5, the Binomial Probability Calculator gives Probability: 0.1172.

Frequently Asked Questions

What conditions must be met for the binomial distribution to apply?
There must be a fixed number of independent trials, each with only two outcomes, and the same success probability p on every trial.
What does C(n,k) mean?
It's the number of combinations of n items taken k at a time — the count of distinct ways k successes can occur among n trials.
What inputs does the Binomial Probability Calculator need?
You'll need to provide: Trials (n), Successes (k), Success probability (p). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Binomial Probability Calculator?
The Binomial Probability Calculator applies the formula exactly as calculated — Binomial PMF: P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ, the probability of exactly k successes in n independent trials with success probability p. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Binomial Probability Calculator free to use?
Yes, the Binomial Probability Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Binomial Probability Calculator

The Binomial Probability Calculator uses a real, verifiable formula — Binomial PMF: P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ, the probability of exactly k successes in n independent trials with success probability p. — so results are accurate every time, not an approximation.