Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Hydrological cycle and measurement of its components
Question Statement:
For station X, the maximum one day rainfall with 25 years return period is 100 mm. The probability of a one day rainfall equal to or greater than 100 mm at station X occurring at least once in 15 successive years is
Options:
(A) 0.458
(B) 0.500
(C) 0.637
(D) 0.990
Official Answer Key:
A
Step-by-Step Solution & Explanation
Annual exceedance probability p = 1/T = 1/25 = 0.04. P(at least once in n=15 yrs) = 1 − (1−p)ⁿ = 1 − (0.96)¹⁵ = 1 − 0.5421 = 0.458. (B) is a rough guess; (C) would result from using p wrongly as 1/15; (D) overestimates by treating events as certain each year.
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