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Binomial Calculator

Interactive probability calculator for binomial distributions

The binomial distribution models the probability of obtaining exactly $k$ successes in $n$ independent Bernoulli trials, each with probability $p$ of success.

Probability Mass Function

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

Key Properties

Mean: $\mu = np$
Variance: $\sigma^2 = np(1-p)$
Mode: $\lfloor (n+1)p \rfloor$ or $\lfloor (n+1)p \rfloor - 1$

Parameters

Total number of independent trials (1-1000)
Please enter a valid number between 1 and 1000
Probability between 0 and 1
Please enter a valid probability between 0 and 1

Calculate Probability Range

Calculate P(k₁ ≤ X ≤ k₂)

Probability Distribution

Click "Calculate & Plot" to generate visualization