Binomial Distribution Calculator

Calculate binomial probabilities for events with two possible outcomes.

Distribution Parameters

Number of Trials (n)*

The total number of independent experiments

Probability of Success (p)*

The probability of success in a single trial

Select Probability Type

Number of Successes (k)*

The number of successful outcomes

The probability mass function of the binomial distribution is:

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Where:

The binomial coefficient is calculated as:

\binom{n}{k} = \frac{n!}{k!(n-k)!}

Mean (μ): n × p = 5.0000

Variance (σ²): n × p × (1-p) = 2.5000

Standard Deviation (σ): √(n × p × (1-p)) = 1.5811

Work with the normal probability distribution.

Work with the Poisson probability distribution.

Calculate hypergeometric probabilities.