1.  

A stray rocket randomly falls in a 10 km 15 km rectangular region. Upon impact, it creates a circular crater of 0.1 km radius. Every object within the crater is expected to be damaged. Within the rectangular region are three assets: a 1 kmx1 km square residential area, an 8 km long pipeline, and a 1 km radius circular plant. These assets have relative locations within the rectangular region shown in the figure below. Make the a priori assumption that the center of the impact area is equally likely to occur anywhere within the rectangular region. (a) Determine the probability that each of the assets will be damaged. (b) Determine the probability that any of the assets will be damaged. (c) If the pipeline is known to have been damaged, what are the probabilities that each of the other two assets has been damaged?