3 ms·
But storms aren't people with randomly distributed cities to flood so you don't get the combinatorial effect. It's not like there are a fixed number of 500 year
by kurthr 9y ago
But storms aren't people with randomly distributed cities to flood so you don't get the combinatorial effect. It's not like there are a fixed number of 500 year storms every 3 years that have to flood a uniformly distributed list of cities. The floods are supposedly independent (even if our estimates of likelihood are bad) so there's no binomial coeeficient.
The simple calculation is P=1-(1-1/500^3)^N and the probability is less than 1:10000 assuming independence and even given 6000 cities of a million people (the entire world population is in a similar city).
If it was birthday like (every possible 500 year storm for 3 years is in a room choosing out of 100 random million person cities), the probablility would be reasonable. You can use a Poisson distribution to estimate the 3 person birthday problem. P=1-exp(-3choose100/500^2)=48%
- roenxi 9y agoActually, in the US it is approximately 1 in 250,000 /assuming independence which is a bit of an assumption/. Obviously, nature doesn't know what a year is so it is totally possible that big storms come in batches. Assuming 1 in 500 year floods are independent, note the ~300 cities in the US [0]. The fact that Huston is a big city doesn't seem relevant to me, because the storm doesn't care. Much like picking a specific number plate, it had to land somewhere. The chance of there being a city in the US which has a 1 in 500 year flood is therefore 60% (300/500) each year. The chance of that city having another flood of similar magnitude in Year 2 is 1/500, because the odds are independent and we started monitoring the city in Year 1. The chance of it flooding again the third year brings the odds down to 1/(500 * 500) = 1 in 250,000. [0] https://en.wikipedia.org/wiki/List_of_United_States_cities_by_population https://en.wikipedia.org/wiki/List_of_United_States_cities_b...