Question

At a Midwestern University, the 450 students in the Business School were classified according to their major within the business school and their gender. The results are:

	Female	Male	Total
Accounting	68	56	124
Administration	91	40	131
Economics	5	6	11
Finance	61	59	120
Other	39	25	64
Total	264	186	450

(a) A student is selected at random. Find the following probabilities; leave your answers in fractional form.

(i) What is the probability that the selected student is a female finance major?

(ii) What is the probability that the selected student is a female or a finance major?

(iii) Given that the selected student is female, what is the probability that she is a finance major?

Answer 1

(i) total number of students = 450

number of female finance major = 61

so, probability = (number of female finance major)/(total number of students)

this implies

= 61/450 or 0.1356

(ii) total number of females + total number of finance major = 264+120 = 384

total number of students = 450

probability = (number of female or finance major)/(total number of students)

this implies

= 384/450

= 64/75 or 0.8533

(iii) number of female finance major = 61 and total number of females = 264

Probability = (number of female and finance majors)/(total number of females)

= 61/264 or 0.2311