How did we do the calculation?

 ((t-b)/t)ⁿ is the formula where t is the total number of possible outcomes, b is the number of bad outcomes, and n is the number of trials (years if we are talking about storms). Probability formulas are useful but they leave me cold and lacking real understanding. I like to see how the calculation works.  Let's see how it works starting with some examples.

If they built the levees out of papiermache and they told us the probability of a catastrophe was 50/50. It would be like tossing a coin.  In year one there is a 50% chance of a hit. In two successive years there is a 1 in 4 chance of avoiding being hit or a 25% chance of tossing two heads in a row. If we hoped to live in the area for ten years we'd have less than a one in a thousand chance of avoiding a hit. (1/2)ⁿ

Now consider a six sided die (one of a pair of dice, not a tool). What is the chance of  not rolling a one in any number of tries. This would be like protecting against a six year storm. Well on the first try it there is a 5/6 chance that we would be safe. The chance of getting a 1 is 1/6 on the first try and the process would have stopped (you rolled a 1 and the city was destroyed). If you have to roll twice you get a 5/6 chance on the first try and then if you didn't lose you play again. You have a 5/6 chance of playing again and if you get a second turn you have a 5/6 chance of surviving to play again. That's a (5/6)²= 69.4% probability that you wont get a 1 on either of two tries. In ten tries the odds that you won't hit a 1 drops to 16% and by the twentieth try you are down to 2%. Digging into what is going on  ((t-b)/t)ⁿ is the formula where t is the total number of possible outcomes, b is the number of bad outcomes, and n is the number of trials (tosses, or years if we are talking about storms)

So let's get back to that 100 year storm. For the storm with a 1% probability of hitting in any given year the the formula reduces to  (.99)ⁿ   assuming you want to live peacefully for n years in the city. It shows you can live here without a catastrophe for 10 years 90% of the time. If you want to stay 20 years, your chances drop to 82%. Forty years will be safe 66% or two thirds of the time. Staying safe for an entire century is unlikely, only 37%, so in two out of every three centuries the city will drown if you build the levees to resist a one hundred year storm.

So if you are willing to roll the dice and are comfortable with these odds then come on down!

If you are an insurance executive you can compute the odds and understand what they mean.  So if you expect the chance of paying the maximum value on your flood insurance policy is 50%, you need to collect 50% plus your costs every 68 years.  So what is my premium? Let's say I want $100,000 to be covered. $100,000 * .5 / 68 + costs =  the premium. It costs $735+costs per year per $100,000 if you really believe you are protecting against a 100 year storm. Who can afford that?