Major Motors sells both new and used cars. Past sales records show the following customer purchasing behaviour: 60% of all sales tend to be of new cars, and 40% of used cars. When a new car is sold, there is a 50% chance that the customer will purchase an extended car warranty. When a used car is sold, there is a 75% chance that the customer will purchase an extended car warranty.

A new customer is about to purchase a car from Major Motors. As the salesman, you would like to look at all possibilities in terms of the person buying a used or new car with or without the extended warranty.

a.Draw a tree diagram to illustrate all possible customer purchase outcomes in terms of the customer buying a used or new car with or without the extended warranty. [3 marks]

b.Find the probability that the new customer will purchase a new car and the extended warranty. [4marks]

c.Find the probability that the new customer will purchase an extended warranty. [4 marks]

d.Determine if the two events "buys a new car" and "purchases an extended warranty" are independent. [4 marks]