Practice Question: Rate of Return for a Flood Event
NCEES Civil PE Specification V.C.: Storm Characteristics
Problem
Municipal records show a flood devastated a rural town 40 years ago. Risk assessors employed by the town have determined that the probability a flood of the same magnitude will not occur over the next 20 years is 80%. In nearly how many years would you anticipate a similar flood event to occur from present?
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% Students Correctly Answered:
42.0%
Solution
Answer: A) 50 years
The probability that an event will not occur in N years is defined by the following equation:
$$ R=\left(1-p\right)^N $$
$$ where\ p=annual\ probability $$
Given the findings of the risk assessors, we are able to solve for the yearly probability of the event:
$$ 0.80=\left(1-p\right)^{20} $$
$$ p=0.011 $$
Calculate the return period based on the annual probability:
$$ T=\frac{1}{p}=90\ yr $$
Calculate the number of years from today when the flood can be expected occur:
$$ n=90\ yr-40\ yr=50\ yr $$
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