Let $X_n$ be a Simple Symmetric Random Walk in 1 dimension, i.e. $X_n=\sum_{i=1}^n e_i$ where $e_i=\pm1$ each w.p. $1/2$. Let $M_{2n}=\max_{0\leq r\leq 2n}X_r$ and let $m_{2n}=\min_{0\leq r\leq2n}X_r$.
Then find $P(X_0=0,M_{2n}\geq a,m_{2n}\leq -b,X_{2n}=0)$ where $a,b\in\mathbb N$.
I have no idea in proceeding with this problem. I think one has to use reflection principle but how can one use it I do not know. Any help?