Binomial Probability Calculator
Calculate binomial probabilities for exactly, at most, or at least $k$ successes over $n$ trials with success probability $p$.
Why binomial probability?
Benefits
- Quickly evaluate discrete probability outcomes.
- Useful for quality checks and experiments.
- Supports exact and cumulative modes.
Common use cases
- Conversion events across a fixed number of users.
- Defect probability in a batch sample.
- Coin flips and Bernoulli trials.
Field guide
n: number of trials (integer).
k: number of successes (integer).
p: probability of success per trial (0–1).
Mode: exactly $k$, at most $k$, or at least $k$.
Formula: $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$.