Our Teacher Gave Us This Little Problem Today. He

Anonymous

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Our teacher gave us this little problem today. He said it requiresthe use of infinite series to solve. Suppose you are playing a game that consists of 4 positions - A, B,C, D. Whenever you're at a position, you roll a loaded die whoseresult determines your next position. From position A: -there is a 1/2 chance you remain at A -there is a 1/4 chance you move to B -there is a 1/12 chance you move C -there is a 1/6 chance you move to D From position B: -there is a 1/3 chance you remain at B -there is a 1/3 chance you move to A -there is a 1/6 chance you move to C -there is a 1/6 chance you move to D Whenever you reach positions C or D, the game is over. Suppose you start at position A, what is the probability you finishat C? To recieve credit for my answer, i have to be able to explain myanswer using infinite series. Thank you very much for any help insolving this problem

 

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