Jane, Dick, and Spot are playing Frisbee. Dick is equally likely to throw to Jane or

Chapter 6, Problem 4

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QUESTION:

Jane, Dick, and Spot are playing Frisbee. Dick is equally likely to throw to Jane or Spot; Jane always throws the Frisbee to Spot; and Spot is three times as likely to bring the Frisbee to Jane as to Dick. In the long run, what is the probability that Dick gets the Frisbee? (Be sure to check that the transition matrix here is regular.)

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QUESTION:

Jane, Dick, and Spot are playing Frisbee. Dick is equally likely to throw to Jane or Spot; Jane always throws the Frisbee to Spot; and Spot is three times as likely to bring the Frisbee to Jane as to Dick. In the long run, what is the probability that Dick gets the Frisbee? (Be sure to check that the transition matrix here is regular.)

ANSWER:

Step 1 of 3

Let the event that the Frisbee is with Jane, Dick, and Spot be denoted by  and respectively.

Given that Dick is equally likely to throw to Jane or Spot, i.e.

Jane always throws Frisbee to Spot, i.e.,

Spot is three times as likely to bring the Frisbee to Jane as to Dick i.e.,

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