12. A statistics instructor wishes to find out the relationship between the classification of a student and the student's grade in the course. The following is a breakdown of three sections of an introductory statistics course: Grade Freshman (Fr) Sophomore Junior (J) Senior (S) Total (So) A 7 10 12 29 B O 26 N 7 10 26 D w UI 4 13 O 4 N 2 8 Total 5 31 29 37 102 a. What is the probability that the student is a junior and makes a B in the course? b. What is the probability that the student does not make an A in the course, given that the student is a senior? c. What is the probability that the student makes a D or F in the course? Econ 302 Summer 2 2021 Midterm Page 10 of 18 d. Let A be the event that a sophomore is taking the course. Let B be the even that the student makes a C in the course. Are the events A and B independent? Are the events A and B mutually exclusive