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. (30 points)

 

a. Construct a transition matrix for the process of soft drink selection. (10 points)

 

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? (5 points)

 

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? (10 points)

 

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 companyâs soft drink products before

purchasing a Pepsi-Cola product again? (5 points)

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Status NEW Posted 02 May 2017 02:05 AM My Price 10.00

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