Find binomial probabilities — the chance of exactly k successes in n trials, plus the cumulative chance. Enter trials, successes, and the success probability.
P(X = k)
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Exactly k successes.Usage Tip
When n is large and p near 0.5, the binomial distribution looks almost like a normal curve.
THE MATH
P(X = k) = C(n, k) × p^k × (1 − p)^(n − k)
mean = np, sd = √(np(1 − p))
mean = np, sd = √(np(1 − p))
The binomial distribution models the number of successes in a fixed number of independent yes/no trials, each with the same probability.
Coin flips and pass/fail tests are classic examples.
Coin flips and pass/fail tests are classic examples.
k must be between 0 and n; p between 0 and 1.
The cumulative chance of k or fewer successes is also shown.
Mean is np and standard deviation is the square root of np(1 − p).
The cumulative chance of k or fewer successes is also shown.
Mean is np and standard deviation is the square root of np(1 − p).