A town is bordered by two rivers as shown in the following figure. Levees A and...

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A town is bordered by two rivers as shown in the following figure. Levees A and B were constructed to protect the town from high water in the rivers. The levees were both designed for floods with return periods of 5 and 10 yr, respectively. Assume that the events of flooding from the two rivers are statistically independent. (a) Determine the probability that the town will encounter flooding in a given year. Town B (b) What is the probability that the town will be flooded in at least 2 of the next 5 yr? (c) Suppose the townspeople desired to reduce the annual probability of flooding to at most 15%. Levee A may be improved to be capable of floods with return periods of 10 or 20 yr with an investment of 5 or 20 million dollars, whereas levee B may be improved for floods with return periods of 20 or 30 yr with corresponding investment of 10 or 20 million dollars. What is the optimal course of action? A town is bordered by two rivers as shown in the following figure. Levees A and B were constructed to protect the town from high water in the rivers. The levees were both designed for floods with return periods of 5 and 10 yr, respectively. Assume that the events of flooding from the two rivers are statistically independent. (a) Determine the probability that the town will encounter flooding in a given year. Town B (b) What is the probability that the town will be flooded in at least 2 of the next 5 yr? (c) Suppose the townspeople desired to reduce the annual probability of flooding to at most 15%. Levee A may be improved to be capable of floods with return periods of 10 or 20 yr with an investment of 5 or 20 million dollars, whereas levee B may be improved for floods with return periods of 20 or 30 yr with corresponding investment of 10 or 20 million dollars. What is the optimal course of action?