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! 
 A: If you were to only base your estimation on the statistic that it rains on 5.4 days in December, then the calculation is short and ends at your first step, i.e. about 17% chance of rain, or 5-to-1 odds.
In reality, rainy days are correlated (positively or negatively), so whether it rained yesterday or the day before would affect these odds, which you could read about in Markov chains.
(Of course, there is also a multitude of other factors involved...)
A: 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 $0.174$.
A: more appropriately you should like to find out the number of christmas days that it has rained on out of a total number of christmas days. You should also try to understand the chances of it raining with different geographical conditions. This would be alot harder to do. Using the data you found you could also try to find the number of days it normally rains for consecutively and then divide your 5.4 days by that then divide by 31 to give you the chance of a rain on a day when the previous days did not have rain. Ultimately it depends on how much data you have, the more data you get the more the probability of it raining on that specific day will increase as all of the geographical data would indicate the likeliness of it raining. However without any other information 17% divided by the average number of consecutive rainy days would be your best bet for the chances of it raining on a random day in december that did not receive rain in the preceeding day.
A: 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).
