Q-5)... 15 marks When students register for online classes, they have 2 options: (a) a basic, free class (b) a premium class with added resources and tools costing $12/month. Based on this year's student data, the school finds that 70% of new students choose the basic, free class. At the end of their first month, students are faced with 3 options: (1) the basic, free class, (ii) the premium class, or (iii) dropping the class altogether. The past year's student data also shows that the proportions of students with the basic, free class in their first month who choose these 3 options are (6) 60% (1) 30% (iii) 10%, respectively. Also, the proportions of students with the premium class in their first month who choose these 3 options are (1) 80% (1) 10% (ill) 10%. (a) (5 pta) Use a tree diagram to find the probability of a student dropping the class at the end of their first month? Define all relevant events and write any probabilities in terms of these events. In solving any part of this question, explicitly write down the formulas and any steps you use. (b) (2 pts) Is dropping the class in the 2nd month independent of having the free class in the 1" month? (c) (4 pts) What is the probability that a student had originally registered to the free class in their first month given that he/she has the premium class in their second month? (a) (4 pts) What is the probability that a student has a premium class in the first month or a premium class in the second month