3. A company rates its performance in a given year as strong, average, or weak. The company has determined that if it has strong performance in a given year, then in the following year it is equally likely to have strong perfor- mance or average performance. If it has average performance in a given year, there is a - probability chance that it will have average performance the following year, a probabiliy that it will have strong performance the following year, and a - probability that it will have weak performance the following year. If it has weak performance in a given year, there is a probability that it will have weak performance the following year, and a 3 probability that it will have average performance the following year. (a) Find the fraction of time that the company has average performance. (b) If the company has strong performance in a given year, how many additional years, on average, will it continue to have strong performance? (c) If the company has average performance in 2010, what is the probability that it will have strong perfor- mance in 2012?