This is a written question, worth 12 points. Write the problem code beside the question number on your answer sheet and print your name and student ID on the top of your answer sheet. Correctly writing your problem code and printing your name in the correct locations is worth 1 point of the 12 total. ALL steps (work) must be shown on your answer sheet to receive full credit. Submitting work which is not your own will result in a grade of 0 on this exam. Problem Code: 1161 A certain company sends 40% of its overnight mail parcels via express mail service E1. Of these parcels, 2% arrive after the guaranteed delivery time (denote the event late delivery by L). Suppose that 50% of the overnight parcels are sent via express mail service E2 and the remaining 10% are sent via E3. Of those sent via E2 only 5% arrive late, whereas 1% of the parcels handled by E3 arrive late. Part a: Draw a tree diagram for this problem. Part b: If a record of an overnight mailing is randomly selected from the company's file, what is the probability that the parcel went via El and was late? Part c: What is the probability that a randomly selected parcel arrived on time? Part d: If a randomly selected parcel has arrived late, what is the probability that is was not sent via E3