A 300 mm 24-hour rainfall has a 100-year return period. What is the probability that a 24-hour rainfall of 300 mm or more will occur at least once in 10 years_____________?
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Answer: B. 1 – (0.99)10
Explanation
The probability of the event not occurring in any single year is one minus the recurrence interval probability. Raising this non-occurrence probability to the power of ten gives the chance of non-occurrence over ten years. Subtracting this ten-year non-occurrence probability from one yields the probability of occurrence at least once. Return periods represent the statistical likelihood of a given magnitude extreme event occurring in any year. Binomial probability distribution models independent repeated trials such as annual flood occurrences. Calculations involving risk and reliability are fundamental tools in modern hydraulic and hydrological design.
Hydrologists use these probability equations to design spillways and urban drainage systems safely. Evaluating risk over a structure's design life helps prevent catastrophic failures during extreme weather events. Clients and regulatory bodies require rigorous risk assessments for major infrastructure projects. Option a represents the probability of the event not occurring at all during the ten year period. Options c and d use incorrect base values that do not correspond to a one hundred year return period. Incorrect formulas fail to properly apply the binomial complement rule for cumulative multi-year risk.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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