5. 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 is as follows: Undergraduate Major Business Engineering Other Totals Intended Full- 352 197 251 800 Enrollment Time Status Part- 150 161 194 505 Time Totals 502 358 445 1,305 a. Develop a joint probability table for these data. b. Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major 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? 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 Fand B independent? Justify your answer. than 10:11