Rat maze?

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A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?

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  • 1 Answer(s)

    x = 0.25 * 5 + 0.25 (x + 8) + 0.25 * 3 + 0.25 (x + 2)
    x = 1.25 + 0.25x + 2 + 0.75 + 0.25x + 0.5
    x = 4.5 + 0.5x
    0.5x = 4.5
    x = 9

    Ralph Aldanese Scholar Answered on 4th March 2016.
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