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 Fret in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3.
A) .7
B) .61
C) .39
D) .21
E) .18

Question

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 Fret in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3.
A) .7
B) .61
C) .39
D) .21
E) .18

Quizplus · Accepted Answer

To find the probability of purchasing Cessy in year 3 given a purchase of Fret in year 1, calculate the transition probabilities over two steps: P(Fret to Cessy in year 2) = 0.3, then P(Cessy to Cessy in year 3) = 0.6. The probability is 0.3 * 0.6 + 0.7 * 0.4 = 0.18 + 0.28 = 0.39.

The Only Car Dealership in a Community Stocks Cars from Two