1. You can make an organized list to show all possible
Because you can roll the numbers 1, 2, 3, 4, 5, and 6 on a number cube, there are 6 possible outcomes. Together, all the possible outcomes of an experiment make up the sample space. 3 2 6 3 2 6
You can make an organized list to show all possible
outcomes of an experiment.

2. Additional Example 1: Problem Solving Application
One bag has a red tile, a blue tile, and a green tile. A second bag has a red tile and a blue tile. Vincent draws one tile from each bag. What are all the possible outcomes? How many outcomes are in the sample space?

3. Additional Example 1 Continued
Solve 3 B G R
Bag 2
Bag 1
Let R = red tile, B = blue tile, and G = green tile.
Record each possible outcome.
The possible outcomes are RR, RB, BR, BB, GR, and GB. There are six possible outcomes in the sample space.

4. Check It Out: Example 1
Darren has two bags of marbles. One has a green marble and a red marble. The second bag has a blue and a red marble. Darren draws
one marble from each bag. What are all the possible outcomes? How many outcomes are in the sample space?

5. Additional Example 2: Using a Tree Diagram to Find a Sample Space
There are 4 cards and 2 tiles in a board game. The cards are labeled N, S, E, and W. The tiles are numbered 1 and 2. A player randomly selects one card and one tile. What are all the possible outcomes? How many outcomes are in the sample space?

6. Check It Out: Example 2
Shauna spins the spinner at left and flips a coin. Complete the tree diagram. What are all the possible outcomes? How many outcomes are in the sample space?

7. Check It Out: Example 2 Continued1 2 3 4
H T
H T
H T
H T
The possible outcomes are 1H, 1T, 2H, 2T, 3H, 3T, 4H, and 4T. There are eight possible outcomes.

8. The Fundamental Counting Principle states that you can find the total number of outcomes for two or more experiments by multiplying the number of outcomes for each separate experiment.

9. Additional Example 3: Application
Carrie rolls two 1–6 number cubes. How many outcomes are possible?

10. Check It Out: Example 3A
Juan tosses a coin and rolls a number cube. How many outcomes are possible?
There are two possible outcomes for the coin. There are six possible outcomes for the number cube.

11. Check It Out: Example 3B
Juan rolls a number cube and spins the spinner shown in Check It Out question 2. How many outcomes are possible?

12. Lesson Quiz for Student Response Systems
1. Three fair coins are tossed. What are all the possible outcomes? How many outcomes are in the sample space?
A. 2 possible outcomes: H, T
B. 4 possible outcomes: HH, HT, TH, TT
C. 6 possible outcomes: HHH, HHT, HTT, THH, TTH, TTT
D. 8 possible outcomes: HHH, HHT, HTT, HTH, THH, THT, TTH, TTT 12 12 12

13. Lesson Quiz for Student Response Systems
2. Sam tosses a coin and rolls a number cube. What are all the possible outcomes? How many outcomes are in the sample space?
A. 8 possible outcomes: H, T, 1, 2, 3, 4, 5, 6
B. 12 possible outcomes: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6
C. 12 possible outcomes: HH, HT, TH,TT, 12, 23, 34, 45, 56, 61, 11, 66
D. 24 possible outcomes: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6, 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T 13 13 13

14. Lesson Quiz for Student Response Systems
3. Bag A contains a red, a blue, and a yellow ball. Bag B contains a white, an orange, and a green ball. Frederica draws one ball from each bag. What are all the possible outcomes? How many outcomes are in the sample space?
A. 9 possible outcomes: RW, RO, RG, BW, BO, BG, YW, YO, YG
B. 9 possible outcomes: RR, BB, YY, WW, OO, GG, RW, BO, YG
C. 6 possible outcomes: RR, RO, RY, WW, WO, WG 14 14 14