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?