A water tower is located in an active earthquake region. When an earthquake occu
ID: 2957079 • Letter: A
Question
A water tower is located in an active earthquake region. When an earthquake occurs, the probability that the tower will fail depends on the magnitude of the earthquake and also on the amount of storage in the tank at the time of shaking of the ground. For simplicity, assume that the tank is either full (F) or half full (H) with relative likelihood of 1 to 3. The earthquake magnitude may be assumed to be either strong (S) or weak (W) with relative frequencies 1 to 9. When a strong earthquake occurs, the tower will definitely collapse regardless of the storage level. However, the tower will certainly survive a weak earthquake if the tank is only half full. If the tank is full during a weak earthquake, it will have a 50-50 chance of survival.
(a) Compute the probability of collapse of the tower due to earthquakes.
(b) If the tower collapsed during a recent earthquake, what is the probability that the tank was full at the time of the earthquake?
Explanation / Answer
given: pro. of strong earth quake= 0.1 pro. of weak earth quake= 0.9 pro. of full tank = 0.25 pro. of half tank =0.75 a) probability of failure of tower = probability(strong earth quake)+pro( weak earth quake) x pro( full tank )x 0.5 = 0.1+0.9x0.25x0.5=0.2125 b) pro. of failure when the tank is full = pro( strong earth quake)x pro( full tank) + pro(weak earth quake)x pro(full tank)x0.5 = 0.1x0.25 + 0.9x0.25x0.5 =0.1375 so the pro of full tank when the failure occurs = 0.1375/0.2125= 0.647
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