Suppose that the entire cola industry produces only two two colas, cola 1 and co

Question

Suppose that the entire cola industry produces only two two colas, cola 1 and cola 2. Given that a person last purchased cola 1, there is a 90% chance that his/her next purchase will be cola 1. Given that a person last purchased cola 2, there is an 80% chance that his/her next purchase will be cola 2. Suppose further that there are 100 million cola customers and that each customer makes one purchase of cola during any week.

(a) Draw by hand a transition diagram for this market share problem. Clearly identify the states of the transition diagram and the variables.

(b) If a person is currently a cola 1 purchaser, what is the probability that he/she will purchase cola 2 three purcases from now?

(c) If a person is currently a cola 2 purchaser, what is the probability that he/she will purchase cola 1 three purcases from now?

(d) In the long run, what fraction of the cola customers will be drinking cola 1?

Explanation / Answer

Suppose that the entire cola industry produces only two two colas, cola 1 and co

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