A dam is said to be designed for a N-year flood if it has a capacity that will be exceeded with probability 1/N in any given year. Assume that successive annual floods are independent. a. An agency designs 10 dams at widely scattered locations for their respective 500-year floods. If occurrences of floods at each of the dams are mutually independent, what is the probability that two or more dams will fail at least once within the next 50 years?
b. In 1999, the 50-year flood was estimated to be a particular size. In the next 10 years, three floods were observed in excess of this size. If the original estimate was correct, what is the probability of such an observation?