Qusetion: An article on vehicle choice behavior gives the following information about the US car and truck market. The ratio of cars to trucks is 36/64. Among the cars sold 42% are made in the US, while 58% are imports. The corresponding percentages for trucks sold are 70% and 30%.

(a) Find the probability that the next auto consumer will buy an imported car. (Hint. 36% of the sales are cars.)

(b) It is also known that 35% of the consumers who get an import choose to lease it, while 20% of those getting a US-made vehicle lease. Make a tree diagram for the experiment that records the decisions made in the various vehicle acquisition stages, which are

(1) car or truck,

(2) US made or imported, and

(3) buy or lease, and mark the given probabilities on the different paths of the tree diagram.

(c) Use the tree diagram to compute the probability that the next auto consumer will choose to lease his/her chosen vehicle.