A car dealership knows from past experience that 10% of the people who come into the showroom and talk to a salesperson will eventually purchase a car. To increase the chances of success, you propose to offer a free dinner with a salesperson for all people who agree to listen to a complete sales presentation. You know that some people will do anything for a free dinner, even if they do not intend to purchase a car. However, some people would rather not spend a dinner with a car salesperson. Thus, you wish to test the effectiveness of this sales promotion incentive. The project is conducted for 6 months, and 40% of the people who purchased cars had a free dinner. In addition, 10%

of the people who did not purchase cars had a free dinner.

The specific questions to be answered are the following:

a. Do people who accept the dinner have a higher probability of purchasing a new car?

b. What is the probability that a person who does not accept a free dinner will purchase a car?