# Three Rooms, Safety, and Death

You have been caught by a gangster who gives you the chance of escaping by playing a simple game. There are 5 rooms, connected in a cycle as $$S-R_1-R_2-R_3-D$$. You are blindfolded. For each room you go, you must choose one door randomly and enter it.

If you reach $$S$$ you are released, but if you reach $$D$$ you are killed. If you start at $$R_1$$, the probability that you will survive the game is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers. Find $$p+q$$.

Note that you have two choices for the door to enter in each room. You can visualize the rooms as vertices of a regular pentagon, which are labeled in order as $$S-R_1-R_2-R_3-D.$$

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