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 would start if it started the previous morning, and 70% of the time it will not start if it did not start the previous morning. Construct the matrix of transition probabilities. What is the probability that it would start tomorrow if it started today? What is the probability that it will start tomorrow if it did not start today?

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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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 would start if it started the previous morning, and 70% of the time it will not start if it did not start the previous morning.

  1. Construct the matrix of transition probabilities.
  2. What is the probability that it would start tomorrow if it started today?
  3. What is the probability that it will start tomorrow if it did not start today?
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