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9-73.

This problem is a checkpoint for finding probabilities. It will be referred to as Checkpoint 9A.

Because students complained that there were not enough choices in the cafeteria, the student council decided to collect data about the sandwich choices that were available. The cafeteria supervisor indicated that she makes $36$ sandwiches each day. Each sandwich consists of bread, a protein, and a condiment. Twelve of the sandwiches were made with white bread, and $24$ with whole-grain bread. Half of the sandwiches were made with salami, and the other half were evenly split between turkey and ham. Two thirds of the sandwiches were made with mayonnaise, and the rest were left plain with no condiment.

1. Organize the possible sandwich combinations of bread, protein, and condiment by making an area model or tree diagram, if possible.

2. Wade likes any sandwich that has salami or mayonnaise on it. Which outcomes are sandwiches that Wade likes? If Wade randomly picks a sandwich, what is the probability he will get a sandwich that he likes? (Hint:You can use W and G to abbreviate the breads. Then use S, T, and H to abbreviate the proteins, and M and P to abbreviate the condiments.)

3. Madison does not like salami or mayonnaise. Which outcomes are sandwiches that Madison likes? If Madison randomly picks a sandwich, what is the probability she will get a sandwich that she likes?

4. If you have not already done so in part (c), show how to use a complement to find the probability Madison gets a sandwich that she likes.

5. Which outcomes are in the event for the intersection of {salami} and {mayonnaise}?

Check your answers by referring to the Checkpoint 9A materials located at the back of your book.

Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 9A materials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

Answers and extra practice are located in the back of your printed textbook or in the Reference Tab of your eBook.
If you have an eBook for CCG, login and then click the following link: Checkpoint 9A: Probabilities with Unions, Intersections, and Complements