Rat maze

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Question: 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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Riddle Discussion

By: MrJJ on 19/7/20

I thought it would be 7 minutes 20 seconds.\n1/4 chance of picking A, 5 mins\n1/4 chance of picking C, 3 mins\n1/12 chance of picking BA, 13 mins\n1/12 chance of picking BC, 11 mins\n1/12 chance of picking DA, 7 mins\n1/12 chance of picking DC, 5 mins\n1/24 chance of picking BDA, 15 mins\n1/24 chance of picking BDC, 13 mins\n1/24 chance of picking DBA, 15 mins\n1/24 chance of picking DBC, 13 mins\nWhen you multiply the chance by the time and add them all together you get 176/24 which is 7 and 1/3 or 7 minutes and 20 seconds.\nNot sure how you get 9 minutes

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