Binomial Probability Calculator

Calculate binomial distribution probabilities. Free online binomial probability calculator.

The Binomial Probability Calculator computes the probability of exactly k successes in n independent trials, each with probability p. Calculate P(X=k), P(X≤k), or P(X≥k) for any binomial scenario. Essential for quality control, genetics, polling, and any situation with repeated binary outcomes.

Common use cases

  • Quality defect probabilities
  • Coin flip and dice problems
  • Genetics inheritance odds
  • Survey success rates
  • Drug trial outcomes

How to use

  1. Enter number of trials (n)
  2. Enter probability of success (p)
  3. Enter number of successes (k)
  4. Select probability type
  5. Click calculate for the result

FAQ

What is binomial distribution?

Distribution of successes in n independent trials, each with success probability p. Examples: coin flips, pass/fail tests.

What is the binomial formula?

P(X=k) = C(n,k) × p^k × (1-p)^(n-k), combining combinations with probability.

What are the requirements?

Fixed number of trials, two outcomes per trial, constant probability, independent trials.

When does binomial approximate normal?

When n is large and p isn't too extreme. Rule of thumb: np ≥ 10 and n(1-p) ≥ 10.