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. If required, round your answers to four decimal places. (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. P(B)=,P(E)=,andP(O)=sotheundergraduatemajorthatproducesthemostpotentia 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? P (Englneering | Full-Time) = (d) If a student was an undergraduate business major, what is the probabilty that the student intends to attend classes full-time in pursuit of an MBA degree? P (Full-Time | Business) = P' (Full-Time I Business) = (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? Justify your answer. (1) P (Full-Time I Business) * P (Full-Time), Therefore, attending Full-Time classes and being an undergraduate business major are independent events. (ii) P (Full-Time / Business) + P (Full-Time). Therefore, attending Full-Time classes and being an undergraduate business major are not independent events. (iii) P (Full-Time | Business) = P (Full-Time), Therefore, attending Full-Time classes and being an undergraduate business major are not independent events. (iv) P (Full-Time I Business) = P (Full-Time). Therefore, attending Full-Time classes and being an undergraduate business major are independent events