please explain step by step

3. A statistics professor believes that there is a relationship between the attendance and the grade on his Midterm test. After examining his records, he produced the following table of probabilities. Student passes the midterm Student fails the midterm Student misses fewer than 5 lectures 0.81 0.02 Student misses 5 or more lectures 0.04 0.13 Fill out the green margins of the table and answer the questions. a) [T, 4 points] Let F = {Student misses fewer than 5 lectures} and M = {Student passes the Midterm}. Determine p(FNM),(p(F'nM'),p(F),p(M). b) [T, 1 point] What percentage of those students who miss fewer than 5 classes are expected to pass the midterm test? Express using the event notation adopted in part (a). c) [T, 1 point] What percentage of those students who miss 5 or more classes are expected to pass the midterm test? Express using the event notation adopted in part (a). d) [2 points] Are F and M independent events? Fully justify your answer. e) [2 points] Are F and M mutually exclusive events? Fully justify your