Question

tudents 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 Full Time 420 394 75 889 Status Part Time 400 591 44 1,035 Totals 820 985 119 1,924 Develop a joint probability table for these data (to 3 decimals). Undergraduate Major Business Engineering Other Totals Intended Enrollment Full-Time Status Part-Time Totals Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students. 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 (to 3 decimals)? 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 (to 3 decimals)? Let A denote the event that 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 A and B independent?

Answer 1

Develop a joint probability table for these data (to 3 decimals).

	Business	Engineering	Other	Totals
Full time	0.218	0.205	0.039	0.462
Part time	0.208	0.307	0.023	0.538
Totals	0.426	0.512	0.062	1

Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students.

Engineering

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 (to 3 decimals)?

0.205/0.462 = 0.443

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 (to 3 decimals)?

0.218/0.426 = 0.512

Let A denote the event that 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 A and B independent?

No, because P(F/B) ≠ P(F)