A problem by Alessio Di Lorenzo

This system depicted on the link below is composed by an entrance ( $I$ ) , two exites ( $U$ ) , and some "deflectors" ( $d$ ). A little ball is put in the entrance. The ball follows the direction of the arrows. When the ball enters a deflector, it continues its trip following one of the 2 possible paths , with equal probability.

If the probability that the ball exits the system through $U_2$ can be written as $\frac{a}{b}$ where $a,b$ are coprime , what's the value of $a+b$ ?

Picture