There are a number of companies that provide a delivery servicefor take away meals. One of the important factors for the customeris the time between placing an order and receiving the meal. Aparticular Thai restaurant use two different delivery companies.Company A delivers 40% of their orders while Company B delivers therest. A survey of customers using the service have indicated theywant their food delivered within 30 minutes. Historically, CompanyB has experienced 10% of their orders taking longer than 30 minutesto deliver while Company A has been late on 15% of theirorders.
a. We will use A to represent the event ‘Company A delivers theorder’ and L to represent the event ‘The meal is delivered late’.Use the correct statistical notation and words to define thecomplement of both A and L. (Use this terminology in your workingthroughout the remainder of this question).
b. Construct a fully labelled probability tree to describe thisproblem with the outcomes and probabilities shown along eachbranch.
c. A customer has just received their order. What is theprobability the order was delivered on time, that is, within 30minutes of placing the order?
d. A customer who contacted the Thai restaurant reportedreceiving their order 45 minutes after placing the order. Whichcompany is most likely to have delivered the order? Useprobabilities to support your conclusion.
e. Considering the probability calculated in part c., should therestaurant owner have any concerns about the reliability (deliverytimes) of the delivery companies they use? Explain.
