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Suppose that a rat is in a maze with four possible directions. If it goes in the first direction, it gets out in three minutes. If it chooses the second direction, it returns ti the starting point in five minutes. If it chooses the third direction, with probability 0.2 it returns to the start in four minutes, and with probability 0.8 it returns to the start in seven minutes. If it chooses the fourth direction, it gets out of the maze in six minutes with probability 0.3 And returns to the maze in eight minutes with probability 0.7. Each time the rat returns it chooses each direction with probability 1/4. What is the expected time until the rat escapes the maze?

Suppose that a rat is in a maze with four possible directions. If it goes in the first direction, it gets out in three minutes. If it chooses the second direction, it returns ti the starting point in five minutes. If it chooses the third direction, with probability 0.2 it returns to the start in four minutes, and with probability 0.8 it returns to the start in seven minutes. If it chooses the fourth direction, it gets out of the maze in six minutes with probability 0.3 And returns to the maze in eight minutes with probability 0.7. Each time the rat returns it chooses each direction with probability 1/4. What is the expected time until the rat escapes the maze?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that a rat is in a maze with four possible directions. If it goes in the first direction, it gets out in three minutes. If it chooses the second direction, it returns ti the starting point in five minutes. If it chooses the third direction, with probability 0.2 it returns to the start in four minutes, and with probability 0.8 it returns to the start in seven minutes. If it chooses the fourth direction, it gets out of the maze in six minutes with probability 0.3 And returns to the maze in eight minutes with probability 0.7. Each time the rat returns it chooses each direction with probability 1/4. What is the expected time until the rat escapes the maze?
Transcribed Image Text:Suppose that a rat is in a maze with four possible directions. If it goes in the first direction, it gets out in three minutes. If it chooses the second direction, it returns ti the starting point in five minutes. If it chooses the third direction, with probability 0.2 it returns to the start in four minutes, and with probability 0.8 it returns to the start in seven minutes. If it chooses the fourth direction, it gets out of the maze in six minutes with probability 0.3 And returns to the maze in eight minutes with probability 0.7. Each time the rat returns it chooses each direction with probability 1/4. What is the expected time until the rat escapes the maze?
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