GATE 2019 CE (CE1) – Question 33
The probability that annual maximum flood discharge exceeds 25000 m³/s at least once in the next five years is 0.25. Find the flood’s return period (years), to one decimal place.
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Correct answer: 17.8 to 18
Explanation
Assume independent annual exceedances of probability 1/T. No exceedance in five years has probability $(1-1/T)^5=1-0.25=0.75$. Thus $$T=\frac1{1-0.75^{1/5}}=17.8852\ \mathrm{years}.$$ Answer **17.9 years**.