If the distribution of $X_1 ,\dots, X_n$ are symmetric about a common median $\theta$, which means for every $X_i$, $$\Pr(X_i \leq \theta-x) = \Pr(X_i \geq \theta +x),$$ where $i = 1, 2,\dots, n$.
May I get the equation $$\Pr(W+Y \leq 2*(\theta - x)) = \Pr(W+Y \geq 2*(\theta + x))$$ if $W$ and $Y$ are drawn from $X_1$, ..., $X_n$ without replacemnt?
Any suggestion will help! Thank you in advance :)