# Thread: How Often Will It Occur? "If there are 131,800 homes & 1 home burns down every 3 yrs"

1. ## How Often Will It Occur? "If there are 131,800 homes & 1 home burns down every 3 yrs"

I'm working on a paper, and want to express how often something will occur. I'm not a math guy (obviously):

If there are 131,800 homes and one home burns down everythree years, how often will any particular home burn assuming each home will only burn once? What ways can I expressthe chances of this occurring? For example, in my simple mind, I get: 3 x 131,800= one time in 395,400 years.

2. Originally Posted by cainweb
I'm working on a paper, and want to express how often something will occur. I'm not a math guy (obviously):

If there are 131,800 homes and one home burns down everythree years, how often will any particular home burn assuming each home will only burn once? What ways can I expressthe chances of this occurring? For example, in my simple mind, I get: 3 x 131,800= one time in 395,400 years.
This is a tricky problem to answer. To me it sounds like an application of a Poisson random variable, which is a random variable describing the probability that an event will occur a certain number of times in a given time interval, given that that event tends to occur at a certain rate, on average.

https://en.wikipedia.org/wiki/Poisso...n_distribution

The example given, about the probability of "k" floods occurring in 100 years, given that floods occur on average once per 100 years, is pretty similar to your problem. I don't think you can say exactly how much time you have to wait before *your* home burns down, or a specific home burns down, given that the fires are random events, but you can say how likely it is that you will get a certain number of fires in a given time interval. From that you could also compute how much time is needed for a > x% chance that all 131,800 homes will have burned once.

3. Originally Posted by cainweb
If there are 131,800 homes and one home burns down everythree years, how often will any particular home burn assuming each home will only burn once?
If "each home will only burn once", then surely "how often...any particular home [will] burn" is "once"...?

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