[问答题]
A rat is placed in the maze shown in the diagram below. The maze has
m9wvuak9:8cr ;v lazqlzj b-4.x-ah* four ro
vyi n+ f5 kf1m7 ,oixcf-+og)koms (A-D) with open doors
o -5k,i1fnm+ oyx+ vic kf)fg7 between the rooms. For example, there is one open door connecting rooms C and D, whereas there are two open doors connecting rooms B and D.
Every minute, a buzzer is sounded which prompts the rat to move to a connecting room. The probability of the room the rat chooses to move to is determined by the number of open doors available to it. Each time the rat moves and chooses a door to pass through, the probability of each available open door is equal.
1. Determine the transition matrix describing the room the rat chooses to move to each time the buzzer sounds.
The rat is initially placed in room C.
2. Find the probability of the rat being in room D after 15 minutes.
