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. OOO Enrollment Part-Time 150 358 Undergraduate Major Business Engineering Other Totals Intended Full-Time 390 197 251 838 161 194 505 Status Totals 540 445 1,343 17 required, round your answers to four decimal places, (a) Develop a joint probability table for these date Undergraduate Major Business Engineering Other Intended Full-Time Enrollment Part-Time Status Totals Totals (b) Use the marginal probabilities of undergraduate major business, engineering, or others to comment on which undergraduate major produces the most potential MBA students PS) - and PO) 50 - Select your answer Is the undergraduate major that produces the most potential MBA students Totals P(E)- 50 (a) Develop a joint probability table for these data. Undergraduate Major Business Engineering Other Intended Full-Time Enrollment Part-Time Status 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(1) - and PCO) Select your answer is the undergraduate major that produces the most potential MBA students (c) 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? P (Engineering Pull Time) (d) If a student was an undergraduate business major, what is the probability that the student intends to attend dasses full-time in pursuit of an MBA degree? P (Pull-Time Business) - (C) Let F denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let 8 denote. the event that the student was an undergraduate business major. Are events and independent? Select your answer Justify your answer. (1) P (Pull Time Business) P (Time). Therefore, attending Full-Time dates and being an undergraduate business major are independent events (1) (pull-Time Buness) (Pull-Time). Therefore, attending Full Time desses and being an undergraduate business major are not independent (W) (Full-Time Business) - (Pub-Time). Therefore, attending Full-Time Casses and being an undergraduate business major are not independent (WP (Tiness) - (Full Time). Therefore, attending Full-Time dasses and being an undergraduate business major are independent events, Select your answer events, events