22. A rat is trapped in a maze. Initially he has to choose one of two directions....
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22. 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, then with probability j he will depart the maze after two minutes of traveling, and with probability f he will return to his initial position after five minutes of traveling. Assuming that the rat is at all times equally likely to go to the left or the right, what is the expected number of minutes that he will be trapped in the maze?
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