Looking for a correct answer on 5.4.12 part c. Thanks in advance! A personnel ma

Question

Looking for a correct answer on 5.4.12 part c.

Thanks in advance!

A personnel manager constructed the table shown here to define nine combinations of talent and motivation. The numbers in the table are the manager's estimates of the probabilities that a mana- gerial prospect will be classified in the respective categories 5.4.12 TALENT Medium .16 .32 .05 Motivation High Medium Low High .05 .19 Low .05 05 .02 Suppose the personnel manager has decided to hire a new manager. Define the following events: A = { Prospect places high in motivation) B Prospect places high in talent) C = { Prospect places medium or better in both categories) D = {Prospect places low in at least one category) E = { Prospect places high in both categories) a. Does the sum of the probabilities in the table equal 1? b. Find the probability of each event defined above. c. Find P(A U B), P(A n B), and P(A U C).

Explanation / Answer

a)from above:

b)P(A U B) =P(A)+P(B)-P(AnB) =0.26+0.35-0.05 =0.56

P(A n B) =0.05

P(A U C) =P(C) (as A is subset of C)

=1-0.02=0.98

talent high medium low total motivation high 0.05 0.16 0.05 0.26 medium 0.19 0.32 0.05 0.56 low 0.11 0.05 0.02 0.18 total 0.35 0.53 0.12 1

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