Answer:
a) 360 mice
b) 364 mice
Explanation:
Assume :
A = number of infected mice , B = number of non-infected mice
P( infected mice overcoming infection ) = 70% = 0.7
P ( Infected mice not overcoming infection ) = 1 - 0.7 = 0.3
P( mice becoming infected ) = 40% = 0.4
P ( mice not becoming infected ) = 1 - 0.4 = 0.6
Number of infected mice = 400
Number of non-infected mice = 1000 - 400 = 600
step 1 ; express the probabilities in matrix form
![P = \left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right]](https://img.qammunity.org/2022/formulas/mathematics/college/ra2vh7x7ozoedezp1qqmwbn2xdv4ddlb9y.png)
![X = \left[\begin{array}{ccc}400\\600\\\end{array}\right]](https://img.qammunity.org/2022/formulas/mathematics/college/e45dwxppn6resrj6ngcp5ezjt0m8bwptsu.png)
step 2 : multiply the matrix above to determine the number of mice that will be infected
a) For next week
PX =
i.e. 360 mice will get infected next week
next 2 week = P ( PX )
=
*
=
![\left[\begin{array}{ccc}364\\636\\\end{array}\right]](https://img.qammunity.org/2022/formulas/mathematics/college/qjz5ew3u4tjdwfuaontv0ykhrg26fjv4a4.png)
b) In 3 weeks time
P ( P(PX) =
*
=
![\left[\begin{array}{ccc}363.6\\636.4\\\end{array}\right]](https://img.qammunity.org/2022/formulas/mathematics/college/f9rgl7yz2sm8n136holexgddy2dpni121y.png)
i.e. 364 mice will get infected in 3 weeks time