1. Boston has two heating services that offer annual service contracts for home heating: Apple Heating and Banana Heating. Currently, 25% of homeowners have service contracts with Apple, 30% have service contracts with Banana, and the remainder do not have service contracts. Both companies launch aggressive advertising campaigns to attract new customers, with following effects on service contract purchases for the next several years: each year 35% of homeowners with no current service contract decide to purchase a contract from Apple and 40% decide to purchase one from Banana. In addition, 10% of the previous customers at each company decide to switch to the other company, and 5% decide they do not want a service contract.

6.1 Draw a transition diagram.

6.2 "Write a" transition matrix.

6.3 What percentage of homes will have service contracts with Apple next year?

6.4 What percentage of homes will have service contracts with Apple next year?