Question

The pattern of sunny and rainy days on a planet has two states. Every sunny day is followed by another sunny day with probability 0.8. Every rainy day is followed by another rainy day with probability 0.6. Today is sunny on the planet. What is the chance of rain the day after tomorrow?

Answer 1

Let S and R denote sunny and rainy days on the planet The transition probability matrix is given by

We have to find the probability of rain after two days. We have to find T²

Hence if today is sunny on the planet, the chance of rain the day after tomorrow is 0.28.