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 likelihoods 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. If the tower collapsed during a recent earthquake, what is the probability that the tank was full at the time of the earthquakeb. Compute the probability of collapse of the tower due to earthquakes.