Customers buy cars from three auto companies. Given the company from which a customer last bought a car, the probability that she will buy her next car from each company is as follows:

a If someone currently owns a company 1 car, what is the probability that at least one of the next two cars she buys will be a company 1 car?

b At present, it costs company 1 an average of $5,000to produce a car, and the average price a customer pays for one is $8,000. Company 1 is considering instituting a five-year warranty. It estimates that this will increase the cost per car by $300, but a market research survey indicates that the probabilities will change as follows:

Should company 1 institute the five-year warranty?

Will Buy Next from . 1 . 2 .3 Last Bought from 80 10 10 Co. 1 Co. 2 Co. 3 .05 85 10 10 20 .70