1. The soft drink market in the United States is quite competitive; the major market shares are held by Coca-Cola Company and Pepsi-Cola Company. 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 companyâs product. An individual who last purchased a Pepsi-Cola product has a 25% chance of next purchasing a Coca-Cola product, a 60% of next purchasing another Pepsi-Cola product, and a 15% chance of purchasing some other soft drink companyâs product. An individual who last purchased a soft drink made by 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 a 25% chance of next purchasing some other soft drink companyâs 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 customerâs next three soft drink purchases will be Coca-Cola products?

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 customerâs 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 companys soft drink products before purchasing a Pepsi-Cola product again?