Four supervisors and 3 engineers are responsible for work at a construction site, and at least 2 supervisors and one engineer have to be present at all times.

(a) Using two coordinates so that \((2,1)\), for example, represents the event that 2 supervisors and one engineer are present, draw a diagram similar to that of Figure 3.1 showing the points of the corresponding sample space.

(b) Describe in words the events which are represented by \(X=\{(2,2),(3,3)\}, Y=\{(2,1),(2,2)\), \((2,3)\}\) and \(Z=\{(2,1),(3,1),(4,1)\}\).

(c) With reference to part (b), express \(X \cup Y\) symbolically by listing its elements, and also express this event in words.

(d) With reference to part (b), are \(X\) and \(Y\) mutually exclusive?

Data From Figure 3.1

Transcribed Image Text:

Figure 3.1 Sample space for the number California (0,2) (0,1) (1,1) of new computer research facilities to be located in Texas (0,0) (1,0) (2,0) and in California Texas