# Three Rooms, Safety, and Death

**Discrete Mathematics**Level 4

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 \(S-R_1-R_2-R_3-D.\)