Floods can occur at any time. If you’re designing something that could be affected by flooding, it’s important to consider the cumulative probability of flooding: that is, how likely that flooding is to occur at some point over its expected lifespan (aka “design life”). Often people are surprised at how likely such an event is!
The probability that an event of a certain size or larger will occur at least once over a given time period is
1 - (1 - \mathrm{AEP})^nwhere AEP is the annual exceedance probability and n is the number of years. If you have an ARI (average recurrence interval) number instead, convert it to AEP first.
For example, imagine that a 24-hour AEP of 1% equated to 100 mm rainfall. Over a 50 year design life, the probability of one or more rainfall events occurring that have 100 mm or more in 24 hours is 1 - (1 - \mathrm{1\%})^{50} = 39.5%.
This formula represents “1 minus the probability that the event does not occur over n years”. In the above example, the probability of a 1% AEP not occurring in 1 year is 99%, and the probability of it not occurring in 50 years is 99%^50. Therefore the probability of it occurring at some point is 1 – 99%^50.
More examples
The cumulative probability of a 100 year ARI event occurring at some point within a 10 year period is 9.5%.
The cumulative probability of a 100 year ARI event occurring at some point within a 100 year period is 63.2%.