Alternative Equation Formats

$${\displaystyle Pr(X\ge <!--\; \ge \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x|X+Y=x+y)=\underset{i=x}{\overset{m}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}\frac{\left(\begin{array}{c}m\\ i\end{array}\right)\left(\begin{array}{c}n\\ x+y-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>i\end{array}\right)}{\left(\begin{array}{c}m+n\\ x+y\end{array}\right)}}$$

$${\displaystyle Pr(X\ge <!--\; \ge \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x|X+Y=x+y)=\underset{i=x}{\overset{m}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}\frac{\left(\begin{array}{c}m\\ i\end{array}\right)\left(\begin{array}{c}n\\ x+y-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>i\end{array}\right)}{\left(\begin{array}{c}m+n\\ x+y\end{array}\right)}}$$

\[ \Pr (X \ge x ~ |~ X + Y = x + y) = \sum ^{m}_{i=x} \frac{ \left( \begin{array}{cc} m \\ i \end{array} \right) \left( \begin{array}{cc} n \\ x + y - i \end{array} \right) }{ \left( \begin{array}{cc} m + n \\ x + y \end{array} \right) } \]