• Hydrologic Risk of Failure for Hydraulic Structures:
• Risk Formula:

$$R = 1 - (1 - P)^n = 1 - \left(1 - \frac{1}{T}\right)^n$$

where:

• $T = 20\text{ years}$ is the design return period $\implies P = \frac{1}{20} = 0.05$
• $n = 10\text{ years}$ is the expected operational lifespan
• Calculation:

$$R = 1 - (1 - 0.05)^{10} = 1 - (0.95)^{10}$$ $$(0.95)^{10} \approx 0.5987$$ $$R = 1 - 0.5987 = 0.4013 = 40.13\% \approx 40\%$$

• Conclusion: Hydrologic risk is 40% (Option 1).

Correct option: (1) 40%

Analyzing the statements in relation to Hydrologic flood routing: channel and reservoir routing:

The correct option is Option 1: Both Statement (I) and Statement (I) are correct.