11-3 Sample Spaces Warm Up 1. A dog catches 8 out of 14 flying disks thrown. What is the experimental probability that it will catch the next one? 2. If Ted popped 8 balloons out of 12 tries, what is the experimental probability that he will pop the next balloon?

11-3 Sample Spaces Problem of the Day How many different types of meat pizzas can be made if the choices of meat topping are pepperoni, sausage, ham, and meatball? (Hint: There can be 1, 2, 3, or 4 toppings on the pizza.) 15 (4 one-topping, 6 two-topping, 4 three- topping, and 1 four-topping) ‏

11-3 Sample Spaces Learn to use counting methods to determine possible outcomes.

11-3 Sample Spaces Vocabulary sample space Fundamental Counting Principle

11-3 Sample Spaces 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. You can make an organized list to show all possible outcomes of an experiment.

11-3 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. What are all the possible outcomes? How many outcomes are in the sample space? Additional Example 1: Problem Solving Application

11-3 Sample Spaces 1 Understand the Problem Rewrite the question as a statement. Find all the possible outcomes of drawing one tile from each bag, and determine the size of the sample space. List the important information: There are two bags. One bag has a red tile, a blue tile, and a green tile. Additional Example 1 Continued The other bag has a red tile and a blue tile.

11-3 Sample Spaces 2 Make a Plan You can make an organized list to show all possible outcomes. Additional Example 1 Continued

11-3 Sample Spaces Solve 3 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. Additional Example 1 Continued BG RG BB RB BR RR Bag 2Bag 1

11-3 Sample Spaces Look Back 4 Each possible outcome that is recorded in the list is different. Additional Example 1 Continued

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11-3 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. What are all the possible outcomes? How many outcomes are in the sample space? Additional Example 2: Using a Tree Diagram to Find a Sample Space Make a tree diagram to show the sample space.

11-3 Sample Spaces Additional Example 2 Continued List each letter of the cards. Then list each number of 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.

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11-3 Sample Spaces In Additional Example 1, there are three outcomes for the first bag and two outcomes for the second bag. In Additional Example 2, there are four outcomes for the cards and two outcomes for the tiles. Cards Tiles First bagSecond bag

11-3 Sample Spaces 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.

11-3 Sample Spaces Carrie rolls two 1–6 number cubes. How many outcomes are possible? Additional Example 3: Application The first number cube has 6 outcomes. The second number cube has 6 outcomes List the number of outcomes for each separate experiment. 6 · 6 = 36 There are 36 possible outcomes when Carrie rolls two 1 – 6 number cubes. Use the Fundamental Counting Principle.

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11-3 Sample Spaces 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 Lesson Quiz for Student Response Systems

11-3 Sample Spaces 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 Lesson Quiz for Student Response Systems

11-3 Sample Spaces 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 Lesson Quiz for Student Response Systems