GATE 2022 CE (CE2) – Question 34
A flood-control structure has life n years and design flood return period T years. For T=n and $n\to\infty$, find hydrologic failure risk (%) to one decimal.
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Correct answer: 62.88 to 63.52
Explanation
The probability of no exceedance in n independent years is $(1-1/T)^n$. With T=n and n tending to infinity, this approaches $e^{-1}$.
Risk is the complementary probability: $100(1-e^{-1})=63.2121\%$. **Answer: 63.2%**.