# Transition probability matrix, weather changes

I am trying to solve the following problem:

and the probability that there will be three sunny days in a row specifically. I know that the answer is $$1/5$$ but I am trying to figure out how to get this answer. Since I do not know what weather it is the 23 december, how can I solve this problem?

• The sentence "under the assumption that there is still a lot of time before Christmas" is a way of hinting that the weather in 23rd of december will be distributed according to the stationary distribution. – E-A Apr 14 at 17:40
• @E-A thanks, I solved it now! – Natalie_94 Apr 15 at 18:24