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Let $X \text{~} \text{Binomial}(n, p)$ where $p \geq 1/2$.
What is $\text{P}[X \mod 2 = 0]$? Is it of the form $1/2 + O(1/2^n)$?
Let $X \text{~} \text{Binomial}(n, p)$.
