 Binomial probability mass

The binomial probability mass at $k$ isfor $K\sim \mathrm{Bin}(n,p)$. Each selected set of $k$ successes has probability $p^k(1-p{)}^{n-k}$ by independence, and the binomial coefficient counts such subsets. For $n=4,p=1/2$, the masses are $(1,4,6,4,1)/16$. They sum to one by the binomial theorem. Endpoint laws $p=0$ and $p=1$ are concentrated at zero and $n$, respectively.