100 year flood 💧

A 100 year flood is one that has a 1% chance of happening in any particular year. That is the level of risk that the government declares as within a flood plain, and requires flood insurance to purchase a government backed mortgage.

You might think that a 100 year flood occurs every one hundred years or your guaranteed a single flood every 100 years but that’s not how probability works. A 100 year flood only has a 63.3% chance of happening at least once each century.

The formula for probability over time is:

C = Chance in percent of winning
T = The number of times your running the probability
P = Percent chance of winning over time

(1 - (1-C) ) ^ T = P

(1- (1 - 0.01) ) ^ 20 = 0.182 or 18.2% flood risk over 20 years.

A 100 year flood plain has a 63.3% chance of flooding over 100 years, 86.6% chance over 200 years, and 95.0% chance over 300 years.