Markov model problem: What is the probability of rain this night?

Question

This is the question:

How do I deal with the statement that 40% of all afternoons are rainy but this month usually only three afternoons are rainy?

How the model should look like?

Answer 1

3 out of 30 days tend to be rainy $\Rightarrow 10\% $ of all days are rainy.
$50\%$ of all rainy days are cloudy $\Rightarrow$ on $5\%$ of all days in the month, it rains and is cloudy.
Also $40\%$ days in the month are cloudy.
You are only concerned about the $40\%$ days, since it is a cloudy day today.

So, probability of rain $=\frac{5\%}{40\%} = \frac{1}{8}$.

Thus, the probability of rain is $\frac{1}{8}$ or $12.5\%$.