Question

A levee was designed to protect against floods with an annual exceedance probability of 0.02. A larger flood would cause the levee to fail. What is the risk that the levee will NEVER fail in the next 20 years?

Answer 1

Answer:

66.76% probability that the levee will NEVER fail in the next 20 years.

Step-by-step explanation:

For each year, there are only two possible outcomes. Either a levee fails during the year, or no levees fail. In each year, the probabilities of levees failing are independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

A levee was designed to protect against floods with an annual exceedance probability of 0.02. This means that $p = 0.02$

What is the risk that the levee will NEVER fail in the next 20 years?

This is $P(X = 0)$ when $n = 20$. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}*(0.02)^{0}*.(0.98)^{20} = 0.6676$

66.76% probability that the levee will NEVER fail in the next 20 years.