A power cell consists of two sub cells, each of which can provide from 0 to 5 volts, regardless of what the other if the sum of the two voltages of the sub cells is at least 6 volts. An experiment consists of measuring and recording the voltages of the two subcells. Let A be the event that the power cell is functional, let B be the event that two subcells have the same voltage, let C be the event that the first subcell has a strictly higher voltage than the second subcell, and let D be the event that the power cell is not functional but needs less than one additional volt to become functional.
a. Define a sample space S for the experiment as a set of ordered pairs that makes it possible for you to express the four sets above as events.
b. Express each of the events A, B, C, and D as sets of ordered pairs that are subsets of S.
c. Express the following set in terms of A, B, C, and/or D: {(x, y) : x = y and x + y ≤ 5}.
d. Express the following event in terms of A, B, C, and/or D: the event that the power cell is not functional and the second subcell has a strictly higher voltage than the first subcell.