Binomial Probability Calculator

How to use this calculator

Enter the number of trials, the number of successes you want and the probability of success in one trial. The probability of exactly that many successes is calculated, plus the expected number.

Formula

P(X = k) = C(n, k) × p^k × (1 − p)^{n − k}

Worked example

3 heads in 10 fair coin flips:

P = 120 × 0.5³ × 0.5⁷ = 11.72%

Quality-control example

If 2% of parts are faulty, the chance a box of 50 has no faulty parts is 0.98⁵⁰ = 36.4%.

Frequently asked questions

When does the binomial distribution apply?

When there is a fixed number of independent trials, each with the same two outcomes (success/failure) and the same probability.

What is the probability of exactly 3 heads in 10 coin flips?

About 11.7%.

How do I get "at most" or "at least" probabilities?

Add the exact probabilities for each value of k in the range.

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