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


Joe wrote:

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 chracteristic of a discrete event is that it is either
present or not present. There are only two possible states at any
point in time. It's like tossing a coin. You either get a heads or a
tails. By definition, a 100 Years Storm is a storm that will occur at
least once in 100 years.

That's not much of a definition. It could mean that the storm happens
every day, or exactly once every hundred years, or anything in between
- which tells us practically nothing about its likelihood.

That means certainty within 100 years, i.e.
probability equals 1 in the elapsed time of 100 years. On any given day
(or any other time interval you want to use) the storm will either be
present or not be present. Only two possible states. Probability for
each is 0.5 (Probability can never be more than 1.0 so probability of
an event in a process that can have only two possible states is one
divided by two, or 0.5). So each day there is some chance that a storm
of 100 years intensity may occur. If the climate data used in
establishing the 100 year storm was distributed normally, that is if
there were a large number of 100 year intervals sampled, and the
occurance of a 100 years storm happened sometimes in year one,
sometimes in year two, etc of the interval the number of intervals
where the storm occured the most would be the 50th year and there would
be proportionately less occurances in all preceding and suceeding
years. If the data actually showed that, then it would be said to
follow a "normal" distribution. If that data follows the standard
binomial the sum of the probabilites will be 0.5 half way through the
whole range of the data, i.e. in this case at the 50 year point.

.

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