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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 'rt never leaves. Complete parts (A) and {B} below. (A) 1What 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. (Type integers or decimals.) Now determine the limiting matrix l3. 'Ul