Question: Structures in a county need to be designed for earthquake loading. After a detailed seismic risk analysis of the county, it is observed that the

Structures in a county need to be designed for earthquake loading. After a detailed seismic

risk analysis of the county, it is observed that the peak ground acceleration A can be mod

eled by an exponential distribution with a mean of 0.2g. IfA exceeds 0.4g, structures in the

county will suffer significant damage. Assume that earthquakes with A exceeding 0.4g

occure once every 15 years in the county, and the damage from different earthquakes is sta

tistically independent.

(a) What is the probability that there will be exactly two earthquakes where A exceeds 0.4g in the next 50 years? (b) What is the probability of significant structural damage in an earthquake? (c) What is the probability of no significant structural damage due to earthquakes in a year? (d) What is the probability of no significant structural damage due to earthquakes in the next 50 years?

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