The Only Car Dealership in a Community Stocks Cars from Two

Short Answer

The only car dealership in a community stocks cars from two manufacturers, Fret and Cessy. The following transition matrix shows the probabilities of a customer purchasing each brand of car in the next year given that he or she purchased that car in the current year. $$\begin{array} { l c c c } \text { From } / & \text { To } & \text { Fret } & \text { Cessy } \\\hline \text { Fret } & & .7 & .3 \\\text { Cessy } & & .4 & .6 \\\hline\end{array}$$
Given that a customer purchased the brand Cessy in the present year (year 1), determine the probability that a customer will purchase Fret in year 3.