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sol1 - MAT 2342 Assignment 1 Solutions Problem 1 In a big...

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MAT 2342 Assignment 1 Solutions Problem 1. In a big city with a population of 1 million people, there are three telephone companies A, B and C, providing phone services to citizens. To determine how loyal customers are to their phone company, a survey has been conducted. The results of the survey are as follows: 80% of the customers who have a contract with company A stay with company A the next year; 10% switch to company B and 10% switch to company C. Similarly, 80% of the customers who have a contract with company B stay with com- pany B the next year; 10% switch to company A and 10% switch to company C. 60% of the customers who have a contract with company C stay with company C the next year; 20% switch to company A and 20% switch to company B. Currently, 350,000 people have a contract with company A, 400,000 people have a contract with company B and 250,000 have a contract with company C. In the questions below you may assume that all people have a contract with one of the three companies at any time, and that no person has a contract with more than one company at the same time. 1. [2 pts.] Mr. X currently has a contract with company C. How likely is it that he is a customer of company B two years from now? 2. [2 pts.] Predict how many people will have a contract with company B two years from now.
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