Students taking a test 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 353 Engineering Other Totals Intended Full-Time Enrollment Status Part-Time Totals 198 252 803 148 162 194 504 501 360 446 1,307 (a) Develop a joint probability table for these data. (Round your answers to three decimal places.) Undergraduate Major Business Engineering Other Totals Intended Enrollment Status Full-Time Part-Time Totals 1.000 (b) Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students. From the marginal probabilities, we can tell that ---Select--- majors produce 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? (Round your answer to three decimal places.) (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? (Round your answer to three decimal places.) (e) Let A 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 A and B independent? Justify your answer. (Round your answers to three decimal places.) P(A)P(B) = and P(A n B) = so the events ---Select--- independent