Binomial Probability

Find the probability of exactly k successes in n independent trials, or at most or at least k, with the binomial formula shown. Try “P(exactly 3 heads in 8 tosses)”.

Try an example:

How the Binomial Probability works

  1. Check the conditions: fixed n, two outcomes, constant p, independent trials.
  2. Use P(X = k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ.
  3. For “at most” or “at least”, add the individual probabilities.

Frequently asked questions

When is the binomial distribution used?

When you count successes in a fixed number of independent trials that each have the same success probability.

What are the mean and variance of a binomial?

Mean = np and variance = np(1 − p).

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