Atsi arrives at a point with three roads. The first road brings him back to the same point after two hours of walk. The second road brings him back to the same point after four hours of travel. The last road leads to the city after three hours of walk. If every time, Atsi chooses one of three roads with equal probability, what is the expected time (in hours) until he arrives to the city?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Atsi arrives at a point with three roads. The first road brings him back to the same point after two hours of walk. The second road brings him back to the same point after four hours of travel. The last road leads to the city after three hours of walk. If every time, Atsi chooses one of three roads with equal probability, what is the expected time (in hours) until he arrives to the city?

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