solution

Alan Resnik, a friend of Ray Cahnman, bet Ray $5 that Ray’s car would not start five days from now (see Problem 14-8).

(a) What is the probability that it will not start five days from now if it started today?

(b) What is the probability that it will not start five days from now if it did not start today?

(c) What is the probability that it will start in the long run if the matrix of transition probabilities does not change?

Problem 14-8

Ray Cahnman is the proud owner of a 1955 sports car. On any given day, Ray never knows whether his car will start. Ninety percent of the time it will start if it started the previous morning, and 70% of the time it will not start if it did not start the previous morning.

(a) Construct the matrix of transition probabilities.

(b) What is the probability that it will start tomorrow if it started today?

 (c) What is the probability that it will start tomorrow if it did not start today?

 
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