# A problem by Alessio Di Lorenzo

Level pending

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

×