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A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 3 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 4 times as likely to watch a comedy as a reality show the next week.

A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 3 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 4 times as likely to watch a comedy as a reality show the next week.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 11.22EP
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A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 3 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 4 times as likely to watch a comedy as a reality show the next week. 1. Find the transition matrix for this Markov chain. ... ... ... 2. Suppose this student's friends estimate that she is four times as likely to watch a comedy as a reality show and that she will not be watching a sporting event. Find the probability vector representing this estimation. [ 1 3. What is the probability that she watches a sporting event two weeks from now? 4. What is the probability that she watches a comedy three weeks from now?
Transcribed Image Text:A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she chooses a comedy one week, then she is equally likely to choose one of the other programs the following week. If she watches a reality show one week, then she is 3 times as likely to watch a comedy as a sports program the next week. If she watches a sports program one week, then she is 4 times as likely to watch a comedy as a reality show the next week. 1. Find the transition matrix for this Markov chain. ... ... ... 2. Suppose this student's friends estimate that she is four times as likely to watch a comedy as a reality show and that she will not be watching a sporting event. Find the probability vector representing this estimation. [ 1 3. What is the probability that she watches a sporting event two weeks from now? 4. What is the probability that she watches a comedy three weeks from now?
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