# Counting experiment and standard error

I have a counting experiment:

Let's say I have N identical bees. I take one of them, expose it to $\gamma$-radiation and look if it has died or survives. If it survives, I count it as 1 count. If it dies, - 0 counts. I do that N times, until I run out of bees. I calculate the probability of death as:

$p=\frac{\sum_{i=1}^{N}n_i}{N}$

where $n_i$ can be either 1 or 0. Now one says, that the standard error on $p$ is

$\Delta p = \sqrt{\frac{p(1-p)}{N}}$

Why? Could somebody point me to some reading materials?