Question

A culvert is designed for a flood magnitude of return period 100 years and has expected life of 20 years. The risk in this hydrologic design is

• A. $1-{0.99}^{20}$
• B. $1-{0.01}^{20}$
• C. $1-{0.09}^{20}$
• D. $1-{0.10}^{20}$

Answer 1

The correct option is A $1-{0.99}^{20}$

The probability of occurrence of an event atleast once over a period of n successive years is called the risk, R. Thus the risk is given by
$R=1-{(1-\frac{1}{T})}^n$
$=1-{(1-\frac{1}{100})}^{20}=1-{0.99}^{20}$