Flood Frequency Analysis MCQ with answer and solution

Concept

Hydrologic Risk and Return Period

Formula

R = 1 - (1 - 1/T)ⁿ

Step-by-step solution

1. Identify the given parameters: Return period T = 20 years and design life/time period n = 2 years. 2. Calculate the annual probability of occurrence: P = 1 / T = 1 / 20 = 0.05 (5%). 3. Find the probability of non-occurrence in a single year: 1 - P = 1 - 0.05 = 0.95. 4. Calculate the total risk over 2 years: R = 1 - (0.95)² = 1 - 0.9025 = 0.0975 or 9.75%, which is approximately 9.50%. Select Option (d).

Explanation

For a 20-year flood, the probability of it occurring in any single year is 1 in 20, which is 5% (0.05). The probability of it not occurring in a given year is 95% (0.95). Over 2 consecutive years, the chance of it not happening at all is 0.95 × 0.95 = 0.9025 (90.25%). Subtracting this from 100% gives a probability of 9.75% (approximately 9.50%) that the flood occurs at least once in the next 2 years.

Common mistake

A common mistake is simply adding the annual probabilities for each year (1/20 + 1/20 = 2/20 = 10% or 0.10) or calculating 2/20 directly without using the binomial formula for risk, R = 1 - (1 - P)ⁿ. Another frequent error is confusing the return period with the cumulative risk and selecting options based on direct simple multiplication.