An escape room participant, named Alice, is trapped in a room containing three doors. Assume that, at all times, Alice equally likely to choose any of the doors. The first door leads to a route that takes Alice to safety after 1 hour. The second door leads to a route that takes her back to the same room after 1 hour. The third door leads to a route that returns her back to the same room after 30 minutes. What is the expected length of time until she reaches safety?

An escape room participant, named Alice, is trapped in a room containing three doors. Assume that, at all times, Alice equally likely to choose any of the doors. The first door leads to a route that takes Alice to safety after 1 hour. The second door leads to a route that takes her back to the same room after 1 hour. The third door leads to a route that returns her back to the same room after 30 minutes. What is the expected length of time until she reaches safety?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An escape room participant, named Alice, is trapped in a room containing three doors. Assume that, at all times, Alice equally likely to choose any of the doors.
The first door leads to a route that takes Alice to safety after 1 hour. The second door leads to a route that takes her back to the same room after 1 hour. The third door leads to a route that returns her back to the same room after 30 minutes. What is the expected length of time until she reaches safety?

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