Question

Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Undergraduate Major Business Engineering Other Totals Intended Enrollment Status Full-Time 371 197 251 819 Part-Time 150 161 194 505 Totals 521 358 445 1,324 If required, round your answers to four decimal places. (a) Develop a joint probability table for these data. Undergraduate Major Business Engineering Other Totals Intended Enrollment Status Full-Time Part-Time Totals (b) Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students. P(B) = , P(E) = , and P(O) = , so business is the undergraduate major that produces the most potential MBA students. (c) If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? P (Engineering | Full-Time) = (d) If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree? P (Full-Time | Business) = (e) Let F denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate business major. Are events F and B independent?

Answer 1

The given information is tabulated as below.

Undergraduate Major/ Intended Enrollment Status	Business(B)	Engineering(E)	Other(O)	Total
Full-Time(F)	371	197	251	819
Part-Time(P)	150	161	194	505
Total	521	358	445	1,324

a) The joint PMF table is given below. (Divide all the cells by 1324)

Major/ Status	B	E	O	Total
F	0.2802	0.1488	0.1896	0.6186
P	0.1133	0.1216	0.1465	0.3814
Total	0.3935	0.2704	0.3361	1.00

b)The marginal probabilities are

Since is the largest,  business is the undergraduate major that produces the most potential MBA students

c) The conditional probability,

d) The conditional probability,

e) From part (d), we see (equivalent to ). Hence events F and B are not independent.