1. Representing Sample Spaces
LESSON 13–1
Representing Sample Spaces

2. Five-Minute Check (over Chapter 12) TEKS Then/Now New Vocabulary
Example 1: Represent a Sample Space
Example 2: Real-World Example: Multi-Stage Tree Diagrams
Key Concept: Fundamental Counting Principle
Example 3: Real-World Example: Use the Fundamental Counting Principle
Lesson Menu

3. Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches.
A. 159 in2
B. 145 in2
C. 135 in2
D. 120 in2
5-Minute Check 1

4. Find the volume of a cone with slant height of 4
Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters.
A cm3
B cm3
C cm3
D cm3
5-Minute Check 2

5. Find the volume of a hemisphere with radius of 6 meters.
A m3
B m3
C m3
D m3
5-Minute Check 3

6. Find the lateral area of a cylinder with radius of 8 feet and height of 12 feet.
A. 84 ft2
B ft2
C ft2
D ft2
5-Minute Check 4

7. Find the surface area of a cone with slant height of 8
Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards.
A yd2
B yd2
C yd2
D yd2
5-Minute Check 5

8. The volume of a sphere is 24,429 cubic inches
The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere?
A. 8.7 in.
B in.
C in.
D in.
5-Minute Check 6

9. Mathematical Processes G.1(E), G.1(G)
Targeted TEKS
Preparation for G.13(A) Develop strategies to use permutations and combinations to solve contextual problems.
Mathematical Processes
G.1(E), G.1(G)
TEKS

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

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

12. 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, B R, B B, R
Example 1

13. 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

14. Represent a Sample Space
Tree Diagram
Example 1

15. One yellow token and one blue token are placed in a bag
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

16. The sample space is the result of 4 stages. ● Dressing (F, R, or BC)
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

17. Multi-Stage Tree Diagrams
Answer:
Example 2

18. 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
Example 2

19. Concept

20. 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 possible color color outcomes
,160 × =
Answer: So, a consumer can create 83,160 different possible cars.
Example 3

21. 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
Example 3

22. Representing Sample Spaces
LESSON 13–1
Representing Sample Spaces