The soft drink market in the United States is quite competitive; the major market shares are held by Coca-Cola Company and Pepsi-ColaCompany. Suppose an individual who last purchased a Coca-Cola product has a 70 % chance of next purchasing another Coca-Cola product, a 20 % chance of next purchasing a Pepsi-Cola product, and a 10 % chance of next purchasing some other soft drink company’s product.  An individual wholast purchased a Pepsi-Cola product has a 25 % chance of next purchasing a Coca-Cola product, a 60% of next purchasing another Pepsi-Colaproduct, and a 15 % chance of purchasing some other soft drink company’s product. An individual who last purchased a soft drink madeby some other company has a 30% chance of next purchasing a Coca-Cola product, a 45% chance of next purchasing a Pepsi-Cola product, and a25% chance of next purchasing some other soft drink company’s product.

a. Construct a transition matrix for the process of soft drink selection.

b. Consider a randomly selected consumer who is currently purchasing a soft drink made by Coca-Cola. What is the probability that each of that customer’s next three soft drink purchases will be Coca-Colaproducts?

c. Consider a randomly selected consumer who is currently purchasing a soft drink made by Coca-Cola. What is the probability that each of that customer’s third soft drink purchases will be a Pepsi-Cola product?

d. Given that the long term steady-state probabilities of soft drink selection is as follows:

Coca-Cola 46.73%      

Pepsi-Cola 39.20%     

Other 14.07%

Suppose a customer just purchased a Pepsi-Cola product. What is the average number of times that customer will purchase either a Coca-Cola product of some other company’s soft drink products before purchasing a Pepsi-Cola product again?