SCHWEITZER 2015 Problem 11

For $[0,1]\subset E\subset [0,+\infty)$ where $E$ is composed of a finite number of closed interval,we start a two dimensional Brownian motion from the point $x<0$ terminating when we first hit $E$ .Let $p(x)$ be the probability of the finishing point being in $[0,1]$ .Prove that $p(x)$ is increasing on $[-1,0)$ .