Explore BrainMass

Explore BrainMass

    Absorbing States Probability Problem

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A mouse, after being placed in one of 4 rooms, will search for cheese in that room. If unsuccessful, after one minute it will exit to another room by selecting a door at random. (All the rooms connect to each other.) A mouse entering the room with the cheese will remain in that room. If the mouse begins in room 3, what is the probability that it will get trapped in the long run? Are there any absorbing states? I know that I have to set up a transition matrix, but I am having trouble after that. Can you help me?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:18 pm ad1c9bdddf
    https://brainmass.com/math/probability/absorbing-states-probability-problem-12486

    Solution Preview

    I have attached the solution to this problem for best formatting (also presented below). I hope you find this helpful.

    RESPONSE:
    Absorbing States Problem

    Solution:

    You have to assume that the cheese is in a particular room, say
    Room 1.

    FROM
    Room(1) Room(2) ...

    Solution Summary

    This solution provides the step-by-step solution of how to solve the absorbing states problem using a transition matrix.

    $2.19

    ADVERTISEMENT