Chapter 2. Two different types of snacks became available around the 1930's in the USA - Fritos Corn Chips in 1932 and Lay's Salted Potato Chips in 1931. They both captivated the consumer markets in slightly different regions. While Frito's were popular across the Southern states, Lay's primarily sold in the Southeastern states. As you can imagine, there was some overlap in their market regions and as both companies grew, they started to compete for market shares in other states. Just for the sake of imagination, let us assume that you are a sales manager working for Mr. Dooley (the inventor of Frito's) in the mid-1930s and that you believe that the probability of a customer purchasing a bag of Frito's versus a bag of Lay's is based upon the customer's most recent purchase in Kansas, where both the companies are planning to expand into. Suppose that the following transition probabilities are observed by your team:

	To
From	Frito's	Lay's
Frito's	0.68	0.32
Lay's	0.42	0.58

1. If a customer who last purchased a bag of Frito's is considered, what is the probability that they purchase Frito's in Period 3?
2. The long-run market share for Frito's in Kansas would be % and for Lay's would be %.
3. Suppose that Mr. Dooley wants to launch a special discount campaign such that it would increase the transitional probability from Lay's to Frito's from 0.42 to 0.48. What would be the new projected market share for Frito's after the campaign? %