Statistics

Binomial Distribution Calculator

Probability of k successes in n trials.

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Results update instantly as you type — no submit needed.

Results
P(X = k)
0.161351
P(X ≤ k)
0.762378
P(X ≥ k)
0.398973
Mean
7
Standard deviation
2.1331

Quick answer

The binomial distribution gives the chance of exactly k successes in n independent trials each with probability p.

P(X=k) = C(n,k) p^k (1−p)^(n−k)

How to use the Binomial Distribution Calculator

  1. 1Enter the number of independent trials.
  2. 2Enter the number of successes you are testing.
  3. 3Enter the success probability as a decimal.

Frequently asked questions

When is binomial appropriate?

Fixed trials, two outcomes, constant probability and independence.

What if n is huge?

Use the normal approximation when np and n(1−p) both exceed 5.