Problem 4 The power supply to a community comes from three sources: electricity, gas, and oil. Let E, G, and 0 denote the events of shortages of each of these sources. It is known that P[E] = 0.15, P[G] = 0.1, and P[O] = 02, Furthermore, if there is a shortage in the oil supply, the probability of an electrical power shortage will be doubled. The shortage of gas (group \"a\" of events) is instead statistically independent of shortages of oil and electricity (group \"b\" of events). (a) What is the probability that there will be a shortage of all three sources? (b) What is the probability that there will be a shortage of at least one of the following sources: gas, electricity? (c) What is the probability that exactly two of the three sources will be short? (d) If there is a shortage of electricity, what is the probability that also gas @ oil will be short