The Transition Matrix Below Shows the Probabilities That Customer Switch

Multiple Choice

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. $$\begin{array}{l}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Next Week }\\\begin{array} { l c c } \text { This Week } & \text { Don's } & \text { Limmer's } \\\hline \text { Don's } & 0.9 & 0.1 \\\text { Limmer's } & 0.2 & 0.8\end{array}\end{array}$$ If a customer shopped at Don's the first week, what is the probability that they are shopping at Limmer's the third week?

A) 0.17
B) 0.34
C) 0.66
D) 0.83
E) none of the above