Binomial distribution variance

To find the variance of a discrete random variable in a binomial distribution, we multiply the expectation of the binomial DRV by the probability of failure (one minus the probability of success).

We can write that as:

\text{for }X\sim B(n,p) \quad Var(X)=E(X)\times (1-p)

As we know that E(X)=np, we can write:

\text{for }X\sim B(n,p) \quad Var(X)=n\,p\,(1-p)