calculate probability for rain Last night was new year's eve, and it poured rain.
A friend said, what are the odds for that?
And me, as a student for probability class, thought it would be easy to calculate.

But so far, I'm kinda confused with how to use known facts in my calculations.
I checked online, and got that my city has $5.4$ days of rain in december.

My first thought was denote $P(\text{rain on any day in december}) = 5.4/31 = 0.174$.
But how do I continue from here? Let's suppose rain days are independent, should I do:

$$P(31.12) P(\text{any other 4 days}) \implies P(\text{rain}) (31-1)C_4 P^{4} (1-P)^{31-5} ? $$

Of course these are very easy assumptions to make. If anyone knows how to actually calculate that, I'll be glad to hear.

Happy New Year!
The 5.4 you get from the website is some average over a certain amount of years of the number of rainy days in December. That does not mean though, that you need to calculate for exactly 5 rainy days. Instead, your first approach seems correct (assuming independence which is probably wrong) and you would conclude that the probability is equal to $0.174$.
So it seems my initial thought was correct: No. of December rainy days / No. of days in December = 5.4 / 31 = 0.174 (While assuming every rainy is independent of the others. Wrong in "real life" terms).