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	352	197	251	800
	Part-Time	150	161	194	505
	Totals	502	358	445	1,305

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) = P(O) =
(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?
(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?
(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

d) If a student was an undergraduate business major, then calculate the probability that the student intends to attend classes full-time in pursuit of an MBA degree P(Full - time | BusesmeBusiness) P(Full - time l Business)- P Business 0.2697 0.3847 0.7012 Hence, the required probability is, 0.7012 e) Let F denote the event that the student intends to attend classes full-time in pursuit ofan MBA degree, and let B denote the event that the student was an undergraduate business major. Are events F and B independent? If F and B are independent, then follow the rule: P(F)P(B) P(F andB) P(F)P(B)- P(F and B) Total Full-Time) Grand Total (Total Businees Grand Total Full-Time Businees Grand Total 800 502 1305 13051305 352 0.6130)0.3847)0.2697 0.2358 0.2697 Hence, F and B are not independent