CEGE 3102-A town is situated between two rivers

A town is situated between two rivers: One and Two. Levees A and B were constructed to protect the town from high water in the two rivers. Levee A was built on River One. Levee A was designed to control a maximum flood with a return period of 5 years. Levee B was built on River Two. Levee B was designed to control a maximum flood with a return period of 10 years. Note that neither of these levees are particularly large.While answering the following questions, assume that the flooding events in the two rivers are statistically independent18.Determine the probability that the town will encounter flooding in any given year. Note, this would occur if the capacity of Levee A were exceeded (i.e. greater than a 5- year flood on River One), or if the capacity of Levee B were exceeded (i.e. greater than a 10-year flood on River Two), or if the capacities both of the levees were exceeded.What is the probability that the town will encounter flooding in at least two of the next five years?Suppose that the townspeople want to reduce the annual probability of flooding to at most 15%. Improvements are expensive. • For \$5, 000, 000 Levee A may be improved to control up to a 10-year flood. • For \$20, 000, 000 Levee A may be improved to control up to a 20-year flood. • For \$10, 000, 000 Levee B may be improved to control up to a 20-year flood. • For \$20, 000, 000 Levee B may be improved to control up to a 30-year flood. What is the minimum cost course of action to achieve the desired reduction in the annual probability of flooding?

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