Completing a Flooding Probability Table

(The instructions here are simply a "review" of those of the previous page. If you know how to determine the probability of, for example a 50 year flood during a 10 year period, skip to the bottom of the page and complete the table.)

Keep in mind that every year the probability (P) of a Maximum Annual Peak Discharge (we'll call this a flood) with a given recurrence interval (RI) is 1 divided by the Recurrence Interval
=  1 / RI

From that it follows that the probability of there NOT being a flood within one year is
P(NOT)  =  (1 - 1 / RI)

Over a period of X years, the probability of there NOT being a flood with a certain recurrence interval is,
P(NOT in X years)  =  P(NOT) X  =  (1 - 1 / RI) X

And finally, the probability of there bing a certain size flood in X years is
P(Within X years)  =  1 - P(NOT in X years)  =  1 - (1 - 1 / RI) X

As an example, let's answer the question: What's the probability a flood with a recurrence interval of 25 years, during a 10 year period?

P(Within 10 years)  =  1 - (1 - 1/25)10 = 1 - 0.66 = 0.33 or 33%

Use the calculator to help you fill in the missing data for the Flooding Probability Table below.

NOTE WELL: Although we should not make predictions about the size of a 1000 year flood, we can determine the probality of it happening over a given period of time.

Recurrence Interval
(years)
Probability each year
P ( in 10 years)
P (in 50 years)
P (in 100 years)
2
50%
 
 
 
10
10%
65.1%
 
 
25
4%
33.5%
87%
5. %
50
1. %
18.3%
63.6%
86.7%
100
1.0%
3. %
39.5%
6. %
1,000
0.1%
1%
4.  %
9.5%
10,000
2. %
0.1%
0.5%
1.0%

Notice that no probability ever reaches 100%. Even the 100 year flood, has much less than a 100% probability of occurring during a 100 year period!

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