Practical situation: I’ve got 120 days of data collected during rainy season. On an average it rained on 52.5 of those days.
- What is the probability of it raining at least once in 30 days?
- 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.