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A mouse is trapped in a labyrinth. Initially it can go to the right or to...

A mouse is trapped in a labyrinth. Initially it can go to the right or to the left. If it goes to the right, it will go through the labyrinth for 3 minutes and then return to its initial position. If it goes to the left, then with probability 1/3, it will leave the labyrinth after the 2 minutes; and with probability 2/3 it will return to the initial position after 5 minutes. Assuming the mouse chooses the right or left randomly with equal chance, calculate:
(a) the average time (in minutes) that the mouse is trapped in the labyrinth.
(b) the variance of the time it stays in the labyrinth.

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