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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 company’s 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 company’s 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 company’s product.
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?
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?
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