Identifying managerial prospects who are both talented and motivated is difficult. A humanresources director constructed the following twoway table to define nine combinations of talentmotivation levels. The number in a cell is the director's estimate of the probability that a managerial prospect will fall in that category. Suppose the director has dccided to hire a new manager.

Define the following events:

A: (Prospect places in high-motivation category]

B: (Prospect places in high-talent category}

C: {Prospect is medium or better in both categories)

D: (Prospect places low in at least one category)

E: (Prospect places highest in both categories]

a. Does the sum of the cell probabilities equal I?

b. List the sample points in each of the events described above and find their probabilities.
C. Find P(AUB), P(AnB), and P(A U C).

d. Find P(Ac ) and explain what this means from a practical point of view.

e. Considcr each pair of events (A and B, A and C, etc.). Which of the pairs are mutually exclusive? Why'?