Problem II. [30 points] A town is protected from high river water by two levees A and B. The levees were designed for floods with return periods of 25 and 50 years, respectively. The probability of failure of both levee systems in any year is 0.002. a) Determine the probability of failure of each of the levees in any year. b) Are events of failure of the two levees statistically independent? Why? c) Determine the probability that the town will encounter flooding in any year, i.e., at least one of the levees fail. d) What is the probability that neither of the levees fail in any year? ) What is the probability that the town will be flooded in at least 2 of the next 25 years? e f) What is the probability that the town is flooded for the first time in the 25th year?

Problem II. [30 points] A town is protected from high river water by two levees A and B. The levees were designed for floods with return periods of 25 and 50 years, respectively. The probability of failure of both levee systems in any year is 0.002. a) Determine the probability of failure of each of the levees in any year. b) Are events of failure of the two levees statistically independent? Why? c) Determine the probability that the town will encounter flooding in any year, i.e., at least one of the levees fail. d) What is the probability that neither of the levees fail in any year? ) What is the probability that the town will be flooded in at least 2 of the next 25 years? e f) What is the probability that the town is flooded for the first time in the 25th year?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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