Re: a simple(?) probability question...
- From: James Waldby <j-waldby@xxxxxxxx>
- Date: Sun, 21 Jan 2007 14:16:18 -0700
Joe wrote:
[...] By definition, a 100 Years Storm is a storm that will occur at....
least once in 100 years. That means certainty within 100 years, i.e.
probability equals 1 in the elapsed time of 100 years.
That doesn't agree with common terminology as stated, for example,
in http://bcn.boulder.co.us/basin/watershed/flood.html and
http://en.wikipedia.org/wiki/100-year_flood . From the former:
The terms "10 year", "50 year", "100 year" and "500 year" floods
are used to describe the estimated probability of a flood event
happening in any given year. [...] A 10 year flood has
a 10 percent probability of occurring in any given year, a 50
year event a 2% probabaility, a 100 year event a 1% probability,
and a 500 year event a .2% probability. While unlikely, it is
possible to have two 100 or even 500 year floods within years or
months of each other.
Given the likelihood of 1% for a 100-year event to occur in a
given year, one could figure 1 - (1-0.01)^50 or ~ .395 likelihood
for it to occur at least once in any given 50-year period, or
1 - (1-0.01)^100 or ~ .634 likelihood for any 100-year period.
A Poisson process (http://en.wikipedia.org/wiki/Poisson_process )
with lambda = 0.01 per year has probability ~ .632 of 1 or more
events occurring in any 100-year period, which is about the same
as for the Bernoulli process mentioned in the preceding paragraph,
just as one would expect for a small probability and many years.
-jiw
.
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