1. Splash Screen

2. Lesson Menu Five-Minute Check (over Chapter 12) CCSS 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

3. Over Chapter 12 5-Minute Check 1 A.159 in 2 B.145 in 2 C.135 in 2 D.120 in 2 Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches.

4. Over Chapter 12 5-Minute Check 2 A.85.8 cm 3 B.64.5 cm 3 C.32.0 cm 3 D.15.05 cm 3 Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters.

5. Over Chapter 12 5-Minute Check 3 A.339.3 m 3 B.360.4 m 3 C.421.5 m 3 D.452.4 m 3 Find the volume of a hemisphere with radius of 6 meters.

6. Over Chapter 12 5-Minute Check 4 A.84 ft 2 B.603.2 ft 2 C.1005.3 ft 2 D.2412.7 ft 2 Find the lateral area of a cylinder with radius of 8 feet and height of 12 feet.

7. Over Chapter 12 5-Minute Check 5 A.93.4 yd 2 B.99.4 yd 2 C.131.9 yd 2 D.142.8 yd 2 Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards.

8. Over Chapter 12 5-Minute Check 6 A.8.7 in. B.18.0 in. C.19.8 in. D.76.4 in. The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere?

9. CCSS Content Standards Preparation for S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively.

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

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

12. 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

13. 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.

14. Example 1 Represent a Sample Space Tree Diagram

15. 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

16. 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.

17. Example 2 Multi-Stage Tree Diagrams Answer:

18. 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?

19. Concept

20. 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 1175364383,160 ××××××= Answer:So, a consumer can create 83,160 different possible cars.

21. 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?

22. End of the Lesson