GATE AG 2016 • Q29 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Analysis of precipitation data

Question Statement:

The maximum one day rainfall depth at 20 year return period of a city is 150 mm. The probability of one day rainfall equal to or greater than 150 mm in the same city occurring twice in 20 successive years is ______

Official Answer Key:

0.18 to 0.19

Step-by-Step Solution & Explanation

Annual exceedance probability p = 1/T = 1/20 = 0.05. The probability of the event occurring exactly r=2 times in n=20 independent years follows the Binomial distribution: P(r=2) = C(20,2)×p²×(1−p)^18 = 190×(0.05)²×(0.95)^18 = 190×0.0025×0.3972 = 0.1887, within the accepted band 0.18–0.19.

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