Calculate the probability of exactly k successes in n independent trials, plus the mean and variance.
| P(X = k) | – |
| Mean | – |
| Variance | – |
Use this calculator for a binomial experiment: n independent yes/no trials with the same success probability p on each trial. Typical cases are coin flips, pass/fail items, or a fixed number of independent Bernoulli trials.
The formulas are: P(X = k) = C(n, k) p^k (1 − p)^{n − k}, mean = n p, and variance = n p (1 − p). Enter p as a proportion between 0 and 1, not a percent. For ten fair coin flips, n = 10, p = 0.5, and k = 4 gives P(X = 4) ≈ 0.2051.
Trials must be independent and p must stay constant. This is the probability of exactly k successes, not at least k.
Trials (n): Number of independent trials. An integer of at least 0.
Success probability (p): Chance of success on one trial, from 0 to 1.
Successes (k): Number of successes whose probability you want. Must not exceed n.
P(X = k): Probability of exactly k successes.
Mean: Expected number of successes, n p.
Variance: Spread of the count, n p (1 − p).
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