A survey of local car dealers revealed that $64\%$ of all cars sold last month had a Green Fang system, $28\%$ had alarm systems, and $22\%$ had both Green Fang and alarm systems.

1. What is the probability one of these cars selected at random had neither Green Fang nor an alarm system?

   Hint (a):

   Make a Venn diagram or two-way table.

2. What is the probability that a car had Green Fang and was not protected by an alarm system?

   Hint (b):

   Use the percentage of cars that have Green Fang and the percentage of cars that have both Green Fang
   and an alarm to find out the percentage of cars with only Green Fang.

3. Are having Green Fang and an alarm system disjoint (mutually exclusive) events?

   Answer (c):

   No, because $22\%$ of the cars had both systems.

4. Use the alternative definition of independence (see the Math Notes box in Lesson 7.2.3) to determine if having Green Fang is associated with having an alarm.