A city is supplied water from two reservoirs A and B. Reservoir A is natural, whereas reservoir B is formed by building a dam. Pipes supplying water from both reservoirs cross an active fault, as shown in the figure below. An earthquake on the fault is expected to produce a 30 km rupture, randomly occurring within the fault with uniform likelihood. If the rupture crosses a pipe, the pipe is expected to collapse and lose its capacity to carry water. Furthermore, in case of an earthquake on the fault, there is probability 0.05 that the dam will fail, in which case reservoir B will be lost. Assume the failure of the dam is statistically independent of the failure of the pipes
a) What is the probability that in case of an earthquake on the faulty the water supply from reservoir B will be lost?
b) What is the probability that in case of an earthquake the city will lose its water supply?