A rat is placed in room F or room B of the maze shown to the right. The rat wanders from room to room until it enters one of the rooms containing food, L or R. Assume that the rat chooses an exit from a room at random and that once it enters a room with food it never leaves

(A) What is the long-run probability that a rat placed in room B ends up in room R?Present the given information in a standard form matrix. Within the group of absorbing states and within the group of nonabsorbing states, from left to right and top to bottom, list L before B, F, and R, list R before B and F, and list B before F

Now determine the limiting matrix

P.