## Binomial Distribution Calculator

Binomial distribution calculator is used to find the probability and cumulative probabilities for binomial random variable given the number of trials ($n$) and probability of success ($p$).

Binomial Distribution Calculator
Number of trials ($n$):
Number of success (x):
Probability of success ($p$):
Result
Mean : $np$
Variance : $np(1-p)$
Probability : P(X = x)
Cumulative Probability : P(X ≤ x)
Cumulative Probability : P(X < x)
Cumulative Probability : P(X ≥ x)
Cumulative Probability : P(X > x)

## Binomial Distribution

The probability mass function of Binomial distribution with parameter $n$ and $p$ is

\begin{aligned} P(X=x)&=\binom{n}{x} p^x q^{n-x},\\ & \quad x=0,1,2,\cdots, n;\\ & \quad 0<p<1,q=1-p \end{aligned}

where

• $n =$ number of trials,
• $x =$ number of successes in $n$ trials,
• $p =$ probability of success,
• $q = 1- p =$ probability of failures.