A note on the binomial distribution motivated by Chvátal's theorem and Tomasewski's theorem

Zheng-Yan Guo, Ze-Chun Hu, Run-Yu Wang

Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$. Chvátal's theorem says that for any fixed $n\ge 2$, as $m$ ranges over $\{0,1,\dots ,n\}$, the probabil…