Flood Risk Over a Multi-Year Period

Mediumprobabilityreturn-periodrisk

A flood threshold has an annual exceedance probability of 1/50 (0.02). Years are independent and the probability is stationary. What is the probability of at least one exceedance during a 30-year period?

A60.0%
B54.5%
C45.5%
D2.0%

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Answer: C. 45.5%

P(at least one) = 1 − (1 − p)ⁿ, with p = 0.02 and n = 30. (0.98)³⁰ = 0.5455, so P = 1 − 0.5455 = 0.4545 = 45.5%. 60% comes from 30/50, which treats a '50-year' event as a schedule and ignores that years can repeat or miss. 54.5% is the probability of NO exceedance (the complement) rather than at least one. 2.0% is only the single-year probability.

P

= 1 - (1 - p)^{n}

= 1 - (0.98)^{30}

= 1 - 0.5455

= 0.4545

\approx 45.5%

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Flood Risk Over a Multi-Year Period

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