A hydrologic structure (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 only by a flood equal oto or greater than N-year flood. The magnitude of the N-year flood is that which is exceeded with probablility 1/N in any given year, assuming the succesive annual floods are independent.
a) What is the probability that exactly one flood equal to or in exces of the 40-year flood will occur in a 40-year period?
b) What is the probability one or more floods will exceed the 40-year in 40 years?
c) If an agency design 20 similar, but independet, hydrologic systems (i.e. systems at widely separated locations), for its particular 40-year flood, what is the distribution of the number of systems that will fail at least once within th fist 40 years after their construction?
d) In 1995 the 40 year flood was estimated to be a particular size. In the subequent 10 years, two floods were observed in excess of that size. Because of this people question the correctness of the original estimate.
1) If the original estimate was correct, what is the probability of 2 such floods in 10 years?
2) If the original estimate was correct, what is the probability of 2 or more such floods in 10 years?