1. Holt CA Course 1 8-4 Sample Spaces SDAP3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome. Also covered: SDAP3.3 California Standards

2. Holt CA Course 1 8-4 Sample Spaces Vocabulary sample space compound event Fundamental Counting Principle

3. Holt CA Course 1 8-4 Sample Spaces Together, all the possible outcomes of an experiment make up the sample space. For example, when you toss a coin, the sample space is landing on heads or tails. A compound event includes two or more simple events. Tossing one coin is a simple event; tossing two coins is a compound event. You can make a table to show all possible outcomes of an experiment involving a compound event.

4. Holt CA Course 1 8-4 Sample Spaces 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. Use a table to find all the possible outcomes. What is the theoretical probability of each outcome? Additional Example 1: Using a Table to Find a Sample Space

5. Holt CA Course 1 8-4 Sample Spaces Let R = red tile, B = blue tile, and G = green tile. Record each possible outcome. Additional Example 1 Continued Bag 1Bag 2 RR RB BR BB GR GB RR: 2 red tiles RB: 1 red, 1 blue tile BR: 1 blue, 1 red tile BB: 2 blue tiles GR: 1 green, 1 red tile GB: 1 green, 1 blue tile

6. Holt CA Course 1 8-4 Sample Spaces Find the probability of each outcome. Additional Example 1 Continued P(2 red tiles) = 1616 P(1 red, 1 blue tile) = 1313 P(2 blue tiles) = 1616 P(1 green, 1 red tile) = 1616 P(1 green, 1 blue tile) = 1616 Bag 1Bag 2 RR RB BR BB GR GB

7. Holt CA Course 1 8-4 Sample Spaces 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. Use a table to find all the possible outcomes. What is the theoretical probability of each outcome?

8. Holt CA Course 1 8-4 Sample Spaces Check It Out! Example 1 Continued Let R = red marble, B = blue marble, and G = green marble. Record each possible outcome. Bag 1Bag 2 GB GR RB RR GB: 1 green, 1 blue marble GR: 1 green, 1 red marble RB: 1 red, 1 blue marble RR: 2 red marbles

9. Holt CA Course 1 8-4 Sample Spaces Find the probability of each outcome. Check It Out! Example 1 Continued P(1 green, 1 blue marble) = 1414 P(1 red, 1 blue marble) = 1414 P(2 red marbles) = 1414 P(1 green, 1 red marble) = 1414 Bag 1Bag 2 GB GR RB RR

10. Holt CA Course 1 8-4 Sample Spaces When the number of possible outcomes of an experiment increases, it may be easier to track all the possible outcomes on a tree diagram.

11. Holt CA Course 1 8-4 Sample Spaces 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. Use a tree diagram to find all the possible outcomes. What is the probability that the player will select the E card and the 2 card? Additional Example 2: Using a Tree Diagram to Find a Sample Space Make a tree diagram to show the sample space.

12. Holt CA Course 1 8-4 Sample Spaces Additional Example 2 Continued List each letter on the cards. Then list each number on the tiles. N 1 2 N1 N2 S 1 2 S1 S2 E 1 2 E1 E2 W 1 2 W1 W2 There are eight possible outcomes in the sample space. 1818 = The probability that the player will select the E and 2 card is. 1818 P(E and 2 card) = number of ways the event can occur total number of equally likely outcomes

13. Holt CA Course 1 8-4 Sample Spaces Check It Out! Example 2 There are 3 cubes and 2 marbles in a board game. The cubes are numbered 1, 2, and 3. The marbles are pink and green. A player randomly selects one cube and one marble. Use a tree diagram to find all the possible outcomes. What is the probability that the player will select the cube numbered 1 and the green marble? Make a tree diagram to show the sample space.

14. Holt CA Course 1 8-4 Sample Spaces Check It Out! Example 2 Continued List each number on the cubes. Then list each color of the marbles. 1 Pink Green 1P 1G 2 Pink Green 2P 2G 3 Pink Green 3P 3G There are six possible outcomes in the sample space. 1616 = The probability that the player will select the cube numbered 1 and the green marble is. 1616 P(1 and green) = number of ways the event can occur total number of equally likely outcomes

15. Holt CA Course 1 8-4 Sample Spaces The Fundamental Counting Principle states that you can find the total number of outcomes for a compound event by multiplying the number of outcomes for each simple event.

16. Holt CA Course 1 8-4 Sample Spaces Carrie rolls two 1–6 number cubes. How many outcomes are possible? Additional Example 3: Recreation Application The first number cube has 6 outcomes. The second number cube has 6 outcomes List the number of outcomes for each simple event. 6 · 6 = 36 There are 36 possible outcomes when Carrie rolls two number cubes. Use the Fundamental Counting Principle.

17. Holt CA Course 1 8-4 Sample Spaces Check It Out! Example 3 A sandwich shop offers wheat, white, and sourdough bread. The choices of sandwich meat are ham, turkey, and roast beef. How many different one-meat sandwiches could you order? There are 3 choices for bread. There are 3 choices for meat. List the number of outcomes for each simple event. 3 · 3 = 9 There are 9 possible outcomes for sandwiches. Use the Fundamental Counting Principle.