Question

Q1

Fifty chief executive officers of small to medium-sized companies were classified according to their gender and functional background as shown in the table below:

Functional Background	Male	Female	Total
Marketing	4	10	14
Finance	11	5	16
Operations	17	3	20
Total	32	18	50

1. If a chief executive is randomly selected from this group what is the probability that the executive is a female?
2. What is the probability that a randomly selected executive from this group is a male whose functional background is marketing?
3. Assume that an executive is selected and you are told that the executive’s functional background was in operations. What is the probability that his executive is a female?
4. Assume that an executive is selected and you are told that the executive is female. What is the probability the executive’s functional area is marketing?
5. Are gender and functional background-independent for this set of executives?

Answer 1

(a) The probability that the executive is a female = 18/50 = 0.36

(b) The probability that the executive is a male whose functional background is marketing = 4/50 = 0.08

(c) The probability that an executive with functional background in operations is a female = 3/20 = 0.15

(d) The required probability

= Number of marketing and female/Number of female = 10/18 = 5/9

(e) No, Gender and functional background are not independent for this set of executives.

As the probability of having a particular function is dependent on the gender of the executive