Water Resources and Environmental Hydraulics · Surface Water Resources · 1 mark · Numerical answer
A six-hour rainfall of 6 cm has a return period of 40 years at a station. Find the probability of a six-hour rainfall of this or greater magnitude at least once in 20 successive years, rounded to three decimal places.
Assuming independent annual exceedances, the annual exceedance probability is $p=1/40$. Independence makes the probability of no occurrence in 20 years $(1-p)^{20}=(39/40)^{20}$. Its complement is $1-(39/40)^{20}=.397312\ldots$,so the answer is **0.397**. Multiplying 20 by p would count expected occurrences rather than this probability.
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