Question 1: (14 marks) a) A researcher at a large department store finds that 25% of customers are coerced into buying an item. The researcher also finds that when coerced to buy an item, the shopper returns the item for refund 30% of the time. If a shopper is not coerced into buying an item then that item is returned 2.5% of the time. i) Construct a fully labelled tree diagram to represent the above information. Hint: Firstly use C to represent the event that a shopper is coerced into buying an item and then use R to represent the event that an item is returned. (3 marks) ii) Identify the branches on your tree diagram (by underlining) where an item is returned and use this to calculate the probability that an item is returned. (2 marks) iii) Given an item is returned, calculate the probability that the shopper had been coerced into buying it. (2 marks) iv) Interpret your answer in part iii) and based upon this suggest how management might use this information to guide staff sales conduct. (2 marks)