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 \(a+b\) ?

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