A metropolitan city derives its electrical power from three generating plants A, B and C. Each plant has a generating capacity of 50 MW (megawatt). The chances that the generating plant will be shut down (for periodic maintenance, due to overload, accidents etc) in any given week are, respectively 5%, 5% and 10%. The operations of plant A and B are related in such a way that in case of shutdown at one plant, there is a probability of 50% that the other plant will also shut down due to overload, whereas the operation of plant C is independent of the other two plants.

(a) During a severe storm, lightning knocked out the power lines from plant A, and repair of the lines will take at least 1 week. What is the chance that the city will suffer a complete blackout (no power) in the week that caused by the storm?

(b) What is the probability that the city will have no power in any given week?

(c) What is the probability that the available power supply to the city is less than or equal to 100 MW in a given week?