Judy Jones Purchases Groceries and Pop Exactly Once Each Week $\mathrm{P}($

Multiple Choice

Judy Jones purchases groceries and pop exactly once each week on Sunday evenings. She buys either Coke or Pepsi only and switches from Coke to Pepsi and vice-versa somewhat regularly. Her purchasing behavior of these two drinks is modeled as a Markov system. Let the transition matrix be:

Let $\mathrm{P}($ Coke $)$ and $\mathrm{P}(\mathrm{Pepsi})$ respectively denote the steady state probability that Judy will buy Coke or Pepsi in the very long run on any week. Which of the following is the correct system of equations to find these steady state probabilities?

A) $\mathrm{P}($ Coke $) * 0.7+\mathrm{P}($ Pepsi $) * 0.4=\mathrm{P}($ Coke $)$ and $\mathrm{P}($ Coke $) * 0.3+\mathrm{P}($ Pepsi $) * 0.6=\mathrm{P}($ Pepsi $)$
B) $\mathrm{P}($ Coke $) * 0.7+\mathrm{P}($ Pepsi $) * 0.3=\mathrm{P}($ Coke $)$ and $\mathrm{P}($ Coke $) * 0.4+\mathrm{P}($ Pepsi $) * 0.6=\mathrm{P}($ Pepsi $)$
C) $\mathrm{P}($ Coke $) * 0.7+\mathrm{P}($ Pepsi $) * 0.4=\mathrm{P}($ Pepsi $)$ and $\mathrm{P}($ Coke $) * 0.3+\mathrm{P}($ Pepsi $) * 0.6=\mathrm{P}($ Coke $)$
D) $\mathrm{P}($ Coke $) * 0.7+\mathrm{P}($ Pepsi $) * 0.4=\mathrm{P}($ Coke $)$ and $\mathrm{P}($ Coke $) +\mathrm{P}($ Pepsi $) =1.0$