Let \(S=[0,5]\) be a sample space containing all possible values of the daily quantity demanded of electric power for a large midwestern city in the summer months. The units of measurement are millions of megawatts, and the capacity of the power grid is five million megawatts. Answer the following questions concerning probability assignments to events in the sample space, \(S\), relating to the daily demand for electric power. Treat the information provided in the questions as cumulative. Justify your answers.

a. Given that \(A=[0,4], B=[3,5], P(A)=.512\) and \(P(B)=.784\), what is the probability that the power demand will be no greater than 4 million megawatts and no less than three million megawatts, i.e., what is the probability of \(A \cap B\) ?

b. What is the probability of the event \(C=[0,3)\) ?

c. Can \(P(D)=.6\) given that \(D=[0,2.5]\) ?

d. Given that \(P([0,2])=.064\), what is the probability of the event \(E=(2,4]\) ?