Bernoulli Distribution

Two categories with probability $p$ and $1-p$ respectively.

For each experiment, the sample space is $\{A, B\}$. The probability for state $A$ is given by $p$ and the probability for state $B$ is given by $1-p$. The Bernoulli distribution describes the probability of $K$ results with state $s$ being $s=A$ and $N-K$ results with state $s$ being $B$ after $N$ experiments,

$$ P\left(\sum_i^N s_i = K \right) = C _ N^K p^K (1 - p)^{N-K}. $$