Understanding 100-Year Flood Probability Calculation

This question asks about the likelihood of a specific type of flood event not happening over a defined period. Let's break down the calculation step-by-step.

Defining the 100-Year Flood Frequency

A flood event described as having a "100-year frequency" means that, on average, such a flood has a 1 in 100 chance of being equaled or exceeded in any given year. This can be represented as a probability:

$P(\text{100-year Flood in one year}) = \frac{1}{100} = 0.01$

This signifies a 1% chance for any single year.

Calculating the Probability of No Flood Occurrence

To determine the chance of the flood not occurring in a single year, we use the concept of complementary probability. The probability of an event not happening is calculated as 1 minus the probability of it happening:

$P(\text{No 100-year Flood in one year}) = 1 - P(\text{100-year Flood in one year})$

$P(\text{No 100-year Flood in one year}) = 1 - \frac{1}{100} = \frac{99}{100} = 0.99$

Therefore, there is a 99% chance that a 100-year flood does *not* happen in any specific year.

Probability Over Multiple Years

The question specifically asks for the probability of this flood not occurring over the next 100 years. Assuming that flood events in different years are independent (meaning one year's event doesn't influence the next), we can calculate the overall probability by multiplying the individual yearly probabilities:

$P(\text{No 100-year Flood over 100 years}) = [P(\text{No 100-year Flood in one year})]^{100}$

Substituting the value we found:

$P(\text{No 100-year Flood over 100 years}) = \left(\frac{99}{100}\right)^{100}$

Performing the Calculation

Now, we calculate the numerical value:

• The expression $\left(\frac{99}{100}\right)^{100}$ is equivalent to $(0.99)^{100}$.
• Using a calculator, we find that $(0.99)^{100} \approx 0.36603234$.

Converting to Percentage Chance

To express this probability as a percentage, we multiply the decimal value by 100:

$0.36603234 \times 100\% \approx 36.6\%$

This calculation demonstrates that the percentage chance of a flood with a 100-year frequency not occurring in the coming 100 years is approximately 36.6%.