Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Analysis of precipitation data
Question Statement:
The analysis of maximum one-day rainfall in a city indicated that a depth of 280 mm has a return period of 50 years. The probability of a one-day rainfall depth equal to or greater than 280 mm in the city occurring two times in 15 successive years is
Options:
(A) 0.032
(B) 0.323
(C) 0.042
(D) 0.272
Official Answer Key:
A
Step-by-Step Solution & Explanation
Annual exceedance probability p = 1/T = 1/50 = 0.02. Using the binomial distribution for exactly k=2 occurrences in n=15 years: P = C(15,2)·p²·(1−p)¹³ = 105 × 0.0004 × (0.98)¹³ = 105×0.0004×0.7690 = 0.0323.
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