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


"Joe" <jconcordia@xxxxxxxxxxx> wrote in message news:1169407963.649149.148000@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

David C. Ullrich wrote:
On 21 Jan 2007 07:56:42 -0800, "Joe" <jconcordia@xxxxxxxxxxx> wrote:


ertug 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 think you have the right answer. The previous respondent disclosed an
elegant statistical procedure,

And he also pointed out that the same reasoning shows that the
probability of a 50-year flood occuring is 50/50 = 1.

You might also note that the same reasoning shows that if the
dam lasts 50 years and a flood is expected every 25 years then
the probability of a flood during the life of the dam is greater
than 1.

Dies this still seem right to you?

however I believe the Poisson model may
not be the best model for the question at hand. The Poisson
distribution is most commonly applied to processes that are considered
"continuous". That is, there is a stream of events occuring and the
Poisson distribution can be used to estimate the number of events
occurring in a period of time or during a set of events of a certain
number, etc. The 100 year storm is not a continuously occuring event.

Huh?

The binomial distribution seems more appropriate. This is like
flipping a coin 100 times. If the coin is completely fair, you would
get 50 heads and 50 tails. i.e the probability of a "yes to the storm"
(heads) or "no to the storm" (tails) in any given year is 50:50 each
year. The cumulative probability ("Z" in the statistical tables) for
a "yes" or a "no" half way through the process (the 100 years) is 0.5
if the process is actually "normally" distributed. I did not study the
climatalogical data to know whether or not it is, but I assume the
people that set the figures for this applied that logic at the time.


************************

David C. Ullrich

I think it would be best to treat The 100 Years Storm as a "discrete
event".

The number of occurences k in the given time interval
is the discrete quantity.
The time when it occurs in the interval is continuous
but that is not what the Poisson distribution is about.
It gives the probability that the number of occurences
in a given time interval is some number k.
Just READ what the Poisson distribution is about:
http://en.wikipedia.org/wiki/Poisson_distribution

Dirk Vdm


.

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