# How to calculate the probability of it raining at least once in a 30 day period?

Practical situation: I’ve got 120 days of data collected during rainy season. On an average it rained on 52.5 of those days.

1. What is the probability of it raining at least once in 30 days?
2. If it rains at least once in 30 days, then what is the probability that it continues to rain for 4 days in a stretch in those 30 days?

My Answer for (1): I considered a Poisson process with $\lambda = 52.5/120 = 0.4375$, calculated the non-occurrence of an event (in this case "no rain") in 30 days and subtracted that value from 1 to get .9999 as the probability of it raining in 30 days.

Please advise if I'm on the right track and also how do we go about part (2) of the question.

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How do you get rain on 0.5 days? Do you have multiple 120 day periods, or are you counting the number of rainfall events per day? –  jbowman May 31 '12 at 12:57

This is not a complete answer, but also too long for a comment and I do hope it answer at least parts of the question.

The Poisson distribution seems to be the wrong way to answer a, since it would theoretically allow for it to rain more than 30 times in 30 days and you seem to have just collected whether it rained at least once for each day. A binomial distribution would be more appropiate.

Another problem is that you basically assume that the weather on each day is independent of the day before. Weather has complex cycles and is certainly autocorellated.

I don't see any way to get more than an approximate answer, but it might help to at least condition the probability of rain on the weather of the day prior. This would be straightforward to implement (ask if necessary) for question 1 and more difficult for question since runs of events are always tricky.

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hmmmm you think it would do any good if we had data from previous year around the same time period as current??? To be frank I feel there is a lot of uncertainity involved and we are making a lot of assumptions here –  Vinay May 31 '12 at 11:58
@jbowman: a day is divided into 4 intervals of 6 hrs each and then rainfall is recorded. –  Vinay May 31 '12 at 14:44