Question

Please show all work and formulas used. Thanks!

A stormwater retention basin is designed to be able to accommodate up to a 50-year storm event. What is the probability that this basin will experience the design storm at least once in the next 5 years? In the next 10 years?

Answer 1

Stormwater retention basin is designed to be able to accommodate up to 50 year storm.

Return period = 50 years

Probability that basin will experience a design storm in a year = 1 / Return period = 1/50 = 0.02

1. At least once in next 5 years.

probability that it will not experience is 1- 0.02 = .98

probability that it will not experience for five years = (1-0.02)⁵ = 0.98⁵

probability that it will experience at least once = 1 - 0.98⁵ = 0.096

2. At least once in next 10 years.

probability that it will not experience is 1- 0.02 = .98

probability that it will not experience for five years = (1-0.02)¹⁰  = 0.98¹⁰

probability that it will experience at least once = 1 - 0.98¹⁰= 0.1829