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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?
in Mathematics by Platinum (129,882 points) | 103 views

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