CCSS Content Standards Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively.

Then/Now You calculated experimental probability. Use lists, tables, and tree diagrams to represent sample spaces. Use the Fundamental Counting Principle to count outcomes.

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

Example 1 Represent a Sample Space 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

Example 1 Represent a Sample Space Table List the outcomes of the first drawing in the left column and those of the second drawing in the top row.

Example 1 Represent a Sample Space Tree Diagram

Example 1 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

Example 1 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

Example 2 Multi-Stage Tree Diagrams CHEF’S SALAD 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.

Example 2 Multi-Stage Tree Diagrams Answer:

Example 2 Multi-Stage Tree Diagrams Answer:

Example 2 A.3 B.4 C.5 D.6 BASEBALL GAME 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?

Example 2 A.3 B.4 C.5 D.6 BASEBALL GAME 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?

Concept

Example 3 Use the Fundamental Counting Principle CARS 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 ,160 ××××××= Answer:

Example 3 Use the Fundamental Counting Principle CARS 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 ,160 ××××××= Answer:So, a consumer can create 83,160 different possible cars.

Example 3 A.3,888 B.3,912 C.4,098 D.4,124 BICYCLES 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?

Example 3 A.3,888 B.3,912 C.4,098 D.4,124 BICYCLES 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?