A certain multinational corporation employs a large number of people from all ov

Question

A certain multinational corporation employs a large number of people from all over the world. It is known that 54% of all people employed by this corporation are from Canada. In addition, 22% of all employees hold management positions. Of all Canadian employees, 3 1% hold management positions. (a) What is the probability that a randomly selected employee is (1) Canadian and holds a management position, (2) Canadian or holds a management position, or both? (b) What proportion of those holding management positions are Canadian? (c) What proportion of all employees hold a management position but are not Canadian? (d) Is the event that a randomly selected employee is Canadian independent of the event that a randomly selected employee holds a management position? Explain (e) Refer to (d). Are these two events mutually exclusive? Explairn.

Explanation / Answer

Let A denote the event of an empoloyee being a Canadian and B denote the event that the empolyee holds management position.

Given P(A) = 0.54 P(B) = 0.22 P(B|A) = 0.31

(a) (1) P(A B) = P(B|A) P(A) = 0.54 * 0.31 = 0.1674

(2) P(A U B) = P(A) + P(B) - P(A B) = 0.54 + 0.22 - 0.1674 = 0.5926

(b) P(A|B) = P(A B) / P(B)

= 0.1674 / 0.22

= 0.761

(c) P(Ac B) = P(B) - P(A B)

= 0.22 - 0.1674

= 0.0526

(d) Since neither P(A|B) and P(B|A) are not equal to P(A) or P(B) respectively, the two events are not independent. Therefore, randomly selecting an employee who turns out to be Canadian and that he holds a management position are not independent.

(e) Since A B is not 0, the events are not mutually exclusive.

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