1. i. ii. iii. iv. V. General questions on probability and statistics: The probability of a flood occurring every year is 0.4. What is the probability of this event occurring in year 2 but not in year 1? What is the probability that a 5-year flood event will occur four times in a 10-year period? What is the probability that a 5-year flood will occur less than four times in a period of 10-years? What is the probability that a 5-year flood will not occur at all in a period of 10-years? A hydrological engineer wants to design a small dam for a flood whose return period is 50 years. What risk are they willing to accept for the flooding to occur in the next 2 years? Problem 2 (25 points) Using the Gutenberg-Richter recurrence law and the coefficient for these geographic regions Compute the following: Location a b Worldwide 7.70 0.90 Western US 5.94 1.14 Eastern US 5.79 1.38 Japan 6.86 1.22 (a) The probability that at least one EQ of magnitude greater than 7.0 will occur in each of the regions in a 10-year period. (b) The probability that at least one EQ of magnitude greater than 7.0 will occur in each region in a 50- year period. (c) The earthquake magnitude that would have a 10% probability of being exceeded at least once in a 50- year period.