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 Full Time 423 394 75 892 Status Part Time 401 594 45 1,040 Totals 824 988 120 1,932 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? Icon Key Previous Question 14 of 15 Next SaveSubmit Test for Grading

Answer 1

Develop a joint probability table for these data.

The table here is given as,

	Business	Engineering	Others	Total
Full time	423	394	75	892
Part time	401	594	45	1040
Total	824	988	120	1932

To find the joint probability table we will simply divide the number of students for each catogery with total number of students(1932).

	Business	Engineering	Others	Total
Full time	0.219	0.204	0.039	0.462
Part time	0.208	0.307	0.023	0.538
Total	0.427	0.511	0.062	1

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 ?

The required probability would be given by,

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 ?

The required probability would be given by,

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?

If the probability , , then events A and B are independent.

In this case we have,

Since these probabilities are not equal, events A and B are not independent.