= Binomial probability mass
= Binomial mass
{synonym}
The <binomial probability mass> at $k$ is
$$
\mathbb P(K=k)=\binom nkp^k(1-p)^{n-k},\qquad k=0,\ldots,n,
$$
for $K\sim\operatorname{Bin}(n,p)$. 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.
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