ANSWER ANY THREE (3) QUESTIONS IN THIS SECTION. QUESTION 1 [20 MARKS] At the end of a semester, the students' grades for Quantitative Methods were tabulated in the following 3 x 2 contingency table to see if there is any association between class attendance and grades received. Grade received No. of Days Absent Pass Fail 0 - 135 110 4 6 36 4 7 - 45 9 6 (a) Calculate the probability that a student selected at random: (i) was absent for less than four days; (2 marks) (ii) was absent for less than seven days; (2 marks) (iii) passed; (2 marks) (iv) passed given that he/she was absent for less than four days; (3 marks) (V ) passed or was absent for less than four days; (4 marks) (vi) passed and was absent for less than four days. (4 marks) (b) Calculate the expected value for the number of days absence