If the last two days have been sunny, then 95% of the time tomorrow will be sunny.
If yesterday was cloudy and today is sunny, then 70% of the time, tomorrow will be sunny.
If yesterday was sunny and today is cloudy, then 60% of the time, tomorrow will be cloudy.
If the last two days have been cloudy, then 80% of the time, tomorrow will be cloudy.
So my tree diagram is as follows. I have completed it for all 16 possibilities, but I only drew up part of it. I just want to know if my approach is correct.
A transition matrix would look like this, and I can fill the rest of the blanks accordingly.
$$ \begin{array}{c|lcr} State & \text{SS} & \text{SC} & \text{CC} & \text{CS}\\ \hline SS & 0.9025 & .0475 & 0.03 & 0.02 \\ SC & ... & ... & ... &...\\ CS & ... & ... & ...&...\\ CC & ...&...&...&... \end{array} $$