A machine is used to produce precision tools. If the machine is in good condition today, then $90\%$ of the

time, it will be in good condition tomorrow. If the machine is in bad condition today, then $80\%$ of the

time, it will be in bad condition tomorrow.

a$.$ What is the transition matrix for the above description?

b$.$ If the machine is in good condition today, what is the probability it will be in bad condition in two

days.

c$.$ Determine the long$-$run fraction of the time that each state