# Calculating the probability of an event occurring in a specific time period

I am confused at how to approach the following question, i.e. what probability formula I am supposed to use.

If the probability of a flood is 0.12 during a year, what is the probability of two floods over the next 10 years...?

I have thought perhaps trying Geometric distribution at first, but it didn't seem to work out properly. I also tried Poisson, but it turned out to be quite a small number... which doesn't seem viable.

So my question is, how can I go about solving this and which probability distribution am I supposed to use?

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If it is only possible to flood once a year if at all (like the Nile) but not twice, then you are looking at a binomial with $n=10$ and $p=0.12$ in either $${n \choose 2}p^2 (1-p)^{n-2}$$ or $$1- p^0 (1-p)^{n-0} - np^1 (1-p)^{n-1}$$ depending on whether you want exactly or at least $2$ floods in $10$ years.

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Yep i solved it like this after a while I got it, cheers –  Jim Nov 8 '13 at 10:58

Correct me if I'm wrong, but wouldn't this just be another Poisson function? Assuming you could have more than 1 flood per year

The expected value --> E(x) = lambda10 = for 10 years = lambda1 * 10 = .12*10 = 1.2 floods in a 10 year period.

So then rerun Poisson's for this new period of 10 years with x = 2 --> P(2) = (1.2^2)e^(-1.2)/2! = .216859 = 21.69% chance of getting EXACTLY 2 floods over 10 years.

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I would try Poisson distribution with lambda = 1.2

Did you try to calculate exactly 2 floods or 2 or more floods?

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I did for exactly 2, n=2 i tried Poisson formula = (1.2^2 * e^(-1.2)) / 2 which = .217, which isn't correct either :( –  Jim Nov 8 '13 at 4:26
That's what I got too. Do you have the answer? P(X>=2) = 1 - (P(0) + P(1)) = 0.337 –  Steve ODonnell Nov 8 '13 at 4:39
I do not have an answer i am afraid, its a practice quiz thing for my exam coming up and it only states whether it's right or wrong... –  Jim Nov 8 '13 at 4:47
0.337 is also incorrect. –  Jim Nov 8 '13 at 4:53
Nevermind its binomial, i just solved it –  Jim Nov 8 '13 at 4:57