Answer Happy

Total Probability A big city is under the influence of several hypothetical seismic sources. The probabilities of earthquake occurrences generated by short-, intermediate and far-distance seismic sources are given as; P(short-distance) 0.2 P(intermediate-distance)-0.4 P(far-distance)-0.4 A statistical study on past earthquakes indicated the following probabilities of large-to-small magnitude events conditioned on above source-to-site distance ranges P(large-magnitude short distance)-0.3 P(moderate-magnitude short-distance)-0.5 P(small-magnitude short-distance)-0.2 P(large-magnitude | intermediate-distance)-0.2 P(moderate-magnitude intermediate distance)-0.4 P/small-magnitude intermediate-distance)-0.4 P(large-magnitude far-distance)-0.1 P(moderate-magnitude | far-distance)-0.3 P/small-magnitude far-distance)-0.6 January 27, 2021 An engineering company in the city is interested in the probability of severe damage caused by earthquakes of different sizes. Their statistical studies suggest that probabilities of damage conditioned on large, moderate and small magnitude events are 0.6, 0.3 and 0.1 regardless of source-to-site distance from the causative seismic source. Compute the probability of severe damage in the city for a future earthquake considering the surrounding seismicity.