Question 1 (18 points) A market research firm is analyzing the behavior of food delivery service users in the Westwood area. The following is known about users in the Westwood area. There are two types of users: UCLA students, and non-UCLA students. 30% of users are UCLA students. For each online order placed by a user, the user orders from UberEats, Doordash or GrubHub. A single order cannot be placed to two delivery services, and an order must be placed to one of these three services. UCLA students order 40% of their orders from Doordash and 40% of their orders from GrubHub. Non-UCLA student users order 50% of their orders from UberEats and 30% of their orders from Doordash. (a) Are the events User is a UCLA student and User is a non-UCLA student user independent? (3 points) (b) Suppose that a user is a UCLA student. What is the probability that an order from this user is placed to UberEats? (3 points) (c) What is the probability that a random order is placed to Doordash? (3 points) (d) An order is placed to Doordash. What is the probability that the order was placed by a UCLA student? (4 points) (e) Suppose that a user places their first order to Doordash, and places their next order to GrubHub. What is the probability that the user is a UCLA student? You may assume that, conditional on the type of user (UCLA student / non-UCLA student), the delivery service is independent from order to order. (5 points)