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GATE 2023 AG – Question 30

Soil and Water Conservation Engineering · Hydrology · 1 mark · Numerical answer

A storm has return period20 years. Find probability it occurs once in five years, to two decimals.

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Correct answer: 0.19 to 0.21

Explanation

For exactly one occurrence and independent years, use the binomial model with p=1/20: $P(X=1)=\binom51(.05)(.95)^4=.2036266$. Rounded, the answer is **.20**. If the wording meant at least one, the result would be $1-.95^5=.226219$,so the official range indicates exactly once.

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