Question: A rat is trapped in a maze. Initially he has to choose one of two directions. If he goes to the right, then he will wander around in the maze for three minutes and will then return to his initial position. If he goes to the left, with probability he will depart the maze after two minutes of traveling, and with probability he will return to his initial position after five minutes of traveling. Assuming that this (dumb) rat is at all times equally likely to go the left or to the right, what is the expected number of minutes that he will be trapped in the maze?

Q: 6.

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