# Math Help - Stochastic Matrix Initial Setup

1. ## Stochastic Matrix Initial Setup

I want to make sure I am setting up the following problem correctly...

Problem
A medical researcher is studying the spread of a virus in a population of 1000 mice. During any week there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. One hundred mice are currently infected with the virus.

The matrix I have is:
$\left(\begin{array}{cc}0.20&0.10\\0.80&0.90\end{ar ray}\right)$

and then for the initial numbers matrix:
$X = \left(\begin{array}{c}100\\900\end{array}\right)$

2. Yes, you are correct.