Content Standards

Mathematical Practices

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

You calculated experimental probability.

• Use lists, tables, and tree diagrams to represent sample spaces.

• Use the Fundamental Counting Principle to count outcomes.

• sample space

• tree diagram

• two-stage experiment

• multi-stage experiment

• Fundamental Counting Principle

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, R B, BR, B B, R

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.

Represent a Sample Space

Tree Diagram

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

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

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.

Multi-Stage Tree Diagrams

Answer:

Multi-Stage Tree Diagrams

Answer:

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?

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?

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.

exterior interior seat engine computer wheels doors possiblecolor color outcomes

11 7 5 3 6 4 3 83,160 × × × × × × =

Answer:

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.

exterior interior seat engine computer wheels doors possiblecolor color outcomes

11 7 5 3 6 4 3 83,160 × × × × × × =

Answer: So, a consumer can create 83,160 different possible cars.

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?

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?