Problem $6(120$ points$)$ A Markov Chain diagram is given in the following.

Given that the first day was a workday, i$.$e$.,$ P$($Day $1=$Workday$)=1,$ answer the following questions.

What is the probability the second day was a Workday? Day $2=$ Workday$)?$

What is the probability the second day was a Day Off? P$($Day $2=$Day Off$)?$

What is the probability the third day was a Workday? P$($Day $3=$ Workday$)?$