1. Sample Space and Experiments

2. Vocabulary sample space tree diagram two-stage experiment multi-stage experiment Fundamental Counting Principle

3. Why do we do this? So that each team has a fair chance – or the same odds of gaining possession of the ball first.

4. Important Vocabulary to know: Experiment: Outcome: Event:

5. Example: How many possible outcomes are there? What are the possible

6. Example 1 One red token and one black token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Represent the sample space for this experiment by making an organized list a table, and a tree diagram. Organized List Pair each possible outcome from the first drawing with the possible outcomes from the second drawing. R, RB, B R, BB, R Table Tree Diagram

7. You Try! One yellow token and one blue token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Choose the correct display of this sample space. A.B. C.D.Y, Y; B, B; Y, B

8. Example 2 A chef’s salad at a local restaurant comes with a choice of French, ranch, or blue cheese dressings and optional toppings of cheese, turkey, and eggs. Draw a tree diagram to represent the sample space for salad orders. The sample space is the result of 4 stages. ●Dressing (F, R, or BC) ●Cheese (C or NC) ●Turkey (T or NT) ●Eggs (E or NE) Draw a tree diagram with 4 stages.

9. Example 2 Multi-Stage Tree Diagrams Answer:

10. You Try! A.3 B.4 C.5 D.6 In the bleachers at a major league game you can purchase a hotdog, bratwurst, or tofu dog. This comes with the optional choices of ketchup, mustard, onions, and/or relish. How many stages are in the sample space?

11. Concept

12. Example 3 New cars are available with a wide selection of options for the consumer. One option is chosen from each category shown. How many different cars could a consumer create in the chosen make and model? Use the Fundamental Counting Principle. exteriorinteriorseatenginecomputerwheelsdoorspossible colorcoloroutcomes 1175364383,160 ××××××= So, a consumer can create 83,160 different possible cars

13. You Try! A.3,888 B.3,912 C.4,098 D.4,124 New bicycles are available with a wide selection of options for the rider. One option is chosen from each category shown. How many different bicycles could a consumer create in the chosen model?