Question: Two professors and 3 graduate assistants are responsible for the supervision of a physics lab, and at least one professor and one graduate assistant have to be present at all times.

1. Using two coordinates so that \((1,3)\), for example, represents the event that one professor and 3 graduate assistants are present, draw a diagram similar to that of Figure 3.1 showing the points of the corresponding sample space.
2. Describe in words the events which are represented by \(B=\{(1,3),(2,3)\}, C=\{(1,1),(2,2)\}\) and \(D=\{(1,2),(2,1)\}\).
3. With reference to part (b), express \(C \cup D\) symbolically by listing its elements, and also express this event in words.
4. With reference to part (b), are \(B\) and \(D\) mutually exclusive?

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