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3. A simple artificial intelligence in a turn-based battle game is in one of three states on any given turn: idle, attack, defend. From one turn to the next, here are the probabilities of the status changes: idle-attack 0.5 idle-defend 0.4 attack-idle 0.2 attack-defend 0.4 defend-idle 0.1 defend-attack 0.9 a) The a.i. charges a "super effective" attack during any turn that it is idle, and it requires three turns before it is ready. What is the chance it will have the super effective attack ready on the third turn from now if it defended on this turn? (No matrices needed.) b) On the current turn, the a.i. is in "attack" state. What is the chance it is in the "attack" state on: (i) next turn? (ii) The second turn from now? (iii) The third turn from now? (Do not use matrices.) c) What proportion of time does the a.i. spend in each state after many turns