Determining Flooding Probabilities (More about the 100-year flood!)

If a stream overflows its banks with a flood that has a Recurrence Interval of 100 years, there is one chance in 100 that a flood of that magnitude will occur each year. That's the 100-year flood. In other words there is a 1/100 (= 0.01 or 1.0 %) probability of flooding of that magnitude or greater in any one year.

If your house is on the 100 year flood plain, a 1% chance of flooding each year doesn't seem too bad. On the other hand, if you have a 30 year mortgage you might want to know the probability of a 100 year flooding event during the 30 year lifetime of your mortgage. Should you buy flood insurance or take your chances? Also, there are other questions you should ask such as how likely is a 100-year type flood during any 10 year period? Or how about during a 100 year period? Again, to answer these questions we must rely of statistics.

First, let's turn the probability statement around. If there is a 1% chance of something happening in a given year, like the 100 year flood, then there is a 99% (=0.99) chance of there NOT being a flood during that year. Statistically, over a 30 year period there is a (0.99)30th chance of there not being a flood. (You'll need to use a calculator to raise 0.99 to the 30th power, which is 0.99 times itself 30 times) (0.99)30th = 0.75 or 75%

A 75% chance of there NOT being a flood also means there is a 25% chance that there WILL be a flood over the 30 year period. Those odds aren't very favorable! Should you buy the flood insurance? Should you move?

Answer these questions.

1. What's the probability of a 25 year flooding event occurring each year?
2. Given that a 25-year flooding event has a probability of 4 % of occurring each year (1/25), what is the probability that a 25-year flood will NOT occurr in a given year?
3. A 25 -year type flood had the probability of 4% (1/25) of occurring in a given year and a 96% probability of NOT occurring (100- 4). What's the probability that there will NOT be a 25 year type flood in a 10 year period? (Note that 4% is the same as 0.4).
4. A 25 -year type flood had the probability of 4% of occurring in a given year and a 96% probability of NOT occurring. There is a 66.5% probability that there will NOT be a 25 year flood in a 10 year period. What's the probability that there WILL be a 25 year flood with a 10 year period?
5. Using what you learned above, what's the probability of there being a 50 year type flood in a 20 year period?

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