Question

A certain plant species has either red (dominant), pink (hybred), or white (recesive) flowers, depending on its genotype. If you cross a pink plant with any other plant, the probability distribution of the offsprings are prescribed by the transition matrix
\[
T:=\left(\begin{array}{ccc}
.5 & .25 & 0 \\
.5 & .5 & .5 \\
0 & .25 & .5
\end{array}\right)
\]
The first column of \(T\) means that if you cross a red with a pink, then \(50 \%\) of the time you'll get a red and \(50 \%\) a pink - and never get a white. The second column gives the result if you cross a pink with a pink (25\% red, \(50 \%\) pink, \(25 \%\) white) while the third column concerns crossing a white with a pink.

In the long run, if you continue crossing the offsprings with only pink plants, what percentage of the three types of flowers would you expect to see in your garden?