A car dealership knows from past experience that 10% of potential customers (that is, persons who walk into the dealership and look at cars) will eventually purchase a car. The dealership has started offering a free dinner with a salesperson to any potential customer who agrees to listen to a complete sales presentation. While the free dinner will not increase the percentage of potential customers who buy cars from 10% (no one will buy a car just for a free dinner), management thinks that it will enable salespersons' to target their effort more effectively. To test the effectiveness of this sales program, a free dinner has been offered for six months. During this period, 40% of the people who purchased cars accepted the free dinner. In addition, 20% of the people who did not purchase cars accepted the free dinner.

a. What is the probability that a person does not accept the free dinner? Justify your answer and show all calculations. (5 points)

b. What is the probability that a person who accepts the free dinner will purchase a car? (5 points)