A community is concerned about its power supply for the coming winter. There are three major sources of power supply, namely electricity, gas, and oil. Let E, G, and O denote the events of shortages...

A community is concerned about its power supply for the coming winter. There are three major sources of power supply,
namely electricity, gas, and oil. Let E, G, and O denote the events of shortages of each of these power sources,
respectively. Their probabilities are estimated to be 0.15, 0.1, and 0.2, respectively. Furthermore, assume that if there is a
shortage in the oil supply, the probability of an electrical power shortage will be doubled, that is, twice the probability of
P(E). The shortage of gas may be assumed to be independent of shortages of oil and electricity.
i. What is the probability that there will be a shortage of all three major sources of power supply?
ii. What is the probability that a shortage will occur in at least one of the following sources: gas, electricity?
iii. What is the probability that exactly two of the three sources of power supply will be short?
iv. If there is a shortage of electricity, what is the probability that gas and oil also will be scarce?