A market survey shows that half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season, while the other half remained loyal to Sorey State. On the other hand, three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State. Set these data up as a Markov transition matrix.
(Let 1 = Sorey State, and 2 = C&T.)

Half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season.

This means half moved from State 1 to State 2.

Three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State.

The rest [tex](1-\frac{3}{4}= \frac{1}{4})[/tex] moved from State 2 to State 1.

The Markov Transition Matrix is presented below:

[tex]\left\begin{array}{ccc}\\\\\\$Sorey State&1\\\\C\&T&2\end{array}\right\left[\begin{array}{ccc}$Sorey State&C\&T\\1&2\\------&------\\\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]

The above is presented for clarity sake. The transition matrix is:

[tex]\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]