Question

Suppose that a city is susceptible to earthquakes, and the Modified Mercalli Intensity of the next earthquake is classified (for simplicity) as VI (or less), VII, VIII, and IX with relative likelihoods 50:30:15:5. Building construction is classified as Good or Poor. 20% of buildings in the city are poorly constructed. Seismic fragility analysis has indicated that poorly constructed buildings are damaged with probabilities 0.05, 0.25, 0.50 and 0.75, respectively, when subjected to intensities of VI (or less), VII, VIII, and IX, respectively. Well-constructed buildings suffer no damage under a VI (or less) event; however, the probability that such a building will be damaged under a VII, VIII or IX event is 0.05, 0.10 and 0.20, respectively.

(a) What is the probability that a well-constructed building will be damaged during the next earthquake?

(b) What proportion of buildings in the city will be damaged during the next earthquake?

(c) If a building is damaged, what is the probability that the building was poorly constructed?

(d) What intensity of earthquake is the source of most losses?

Answer 1