A certain model car comes in a two-door version, a four-door version, and a hatchback version. Each version can be equipped with either an automatic transmission or a manual transmission. The accompanying table gives the relevant proportions for purchases. A customer who has purchased one of these cars was randomly selected. a. What is the probability that this customer has purchased a 4-door automatic car? b. Given that a customer purchased a four-door car, what is the probability that it has an automatic transmission? c. Given that a customer purchased a manual transmission car, what is the probability that it is a hatchback? d. Given that a customer did not purchase a hatchback, what is the probability that the car has a manual transmission? e. Given that a customer purchased a two-door or a four door, what is the probability that the car has an automatic transmission? g. What is the probability that a customer purchased a hatchback, a two-door, or a four-door model? Two-Door Four-Door Hatchback Automatic .32 .27 .18 Manual .08 .04 .11 f. What is the probability that a customer purchased a 4-door or a manual transmission