Question

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A system (e.g. a dam or a dike) is said to be designed for the N-year flood if it has a capacity which will be exceeded by a flood equal or greater that the N-year flood. The magnitude of the N-year flood. The magnitude of the N-year flood is that which is exceeded with probability 1/N in any given year. Assume that successive annual floods are independent. a)- What is the probability that exactly one flood equal to or in excess of the "50-year flood" will b)- What is the probability that exactly three floods will equal or exceed this 50-year flood in 50 c)-What is the probability one or more floods will equal or exceed the 50-year flood in 50 years? occur in a 50-year period? years? Hint: this is most easily calculated as 1-P(no floods exceed) d)- If each of 20 independent systems i.e. systems at widely scatter locations - is designed by an agency for its particular 500-year flood, what is the distribution of the number of systems which will fail at least once within the first 50 years after construction? Assume that (1 -)" #1-xn İfxn << 1 . Hint: what is the probability that any one system will not fail in 50 years? e)- In 1958, the 50-year flood was estimated to be a particular size. In the next 10 years, two floods were observed in excess of that size. If the original estimate was correct, what is the probability of such an observation? Such a rare event may be so unlikely that the engineer prefers to believe (i.e. act as if) his original estimate was wrong.

Answer 1