Re: a simple(?) probability question...

On Feb 10, 1:47 pm, "Joe" <jconcor...@xxxxxxxxxxx> wrote:
On Jan 21, 6:51 am, ertug <mail676...@xxxxxxxxxxxx> wrote:

hi,

do you have an idea about this question?

* a river dam has a projected life of 50 years. What is the probability that a hundred-year flood will occur once during the life of the dam?

it is apparently simple and i guess the answer is 50/100 = 0.5; but i am not quite sure and thought there is a catch.

So, do you agree with my answer?

I have been thinking about this question some more and again come to
the conclusion that your answer is correct, i.e. probability is 0.5 as
you calculated.

The rationale for this is based on two essential propositions:

1. The 100 year storm is a storm that is expected to occurr at least
once in 100 years.

This is wrong (or muddled wording at best). The correct statement is
that the expected number of occurrences in 100 years is one. This
means that if you could replay history over and over then *on average*
there would be one occurrence in any given 100 year interval.
Sometimes there would be none, sometimes exactly one, and, with
increasing rarity, sometimes two, three, four, etc.

The accepted definition for "expected" in this case
means that there is certainty for one storm,
i.e. probability equals 1.0 for a storm within the century.

This is wrong. The fact that the expected number of occurrences in 100
years is one does *not* imply that the storm is certain to occur
within a century.

As a
comment, I would suggest there is a corollary proposition; the
probability that two storms exceeding the threshold intensity would
occur in a single 100 year period is so low that it can be excluded
from the analysis.

This is wrong. You think that if the storm occurs in the year 2000
then there is some memory of this event 100 years later, such that the
probability of the storm happening in 2099 is ignorably small but the
probability in 2100 is not so?


2. There is no particular force in nature that would make the
occurance of the 100 year storm more likely in any selected year or
other period within the century.

This is a reasonable assumption, and is indeed the assumption that
underlies both the Poisson and binomial models.

The term for this is that the storms
are disjointed events.

Really?


Given these two factors, the probability is a simple calculation of
1/100 times 50, which supports your original conclusion.

Application of any other probability density function ...

You have not proposed or applied any "probability density function".

... would violate
the stated propositions. For example the Poisson function that
indicates a probability in the range of only 0.6 for the occurance of
a storm in the 100 year span violates proposition #1.

Since your proposition #1 is incorrect this is hardly a problem.

Likewise since
it also indicates the probability of a storm during the first 50 years
as only in the range of 0.3 it violates proposition #2. If that
probability were correct, there would be some greater tendency to have
this storm in the latter years of the century rather than in the early
years. There is no natural reason to expect that.

The Poisson process does *not* predict a greater tendency for the
storm to occur at some particular time. Quite the opposite: it treats
every moment as identical, and every equal time interval as identical.


This analysis must be tempered by the fact that there is no way to
test the validity of the probability estimates. Storm data sets for
intervals of 100 years are not available for a large number of century
time frames. The propositions set forth above are only subjective and
intuitive notions. However there is actual engineering practice to
application of 100 year storm criteria. In that practice real weather
data is examined for the region in question and storm intensity values
are applied to engineering designs consistent with the above
propositions.

Joe


.

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