10-3 Sample Spaces These are the notes that came with the teacher guide for the textbook we are using as a resource. These notes may be DIFFERENT than the notes we take in class if your teacher is in class, but should give you an idea of the concepts if you are struggling to understand them.

10-3 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?

10-3 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?

10-3 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.)

10-3 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) ‏

10-3 Sample Spaces Learn to use counting methods to determine possible outcomes.

10-3 Sample Spaces Vocabulary sample space Fundamental Counting Principle

10-3 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.

10-3 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? Example 1: Problem Solving Application

10-3 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. Example 1 Continued The other bag has a red tile and a blue tile.

10-3 Sample Spaces 2 Make a Plan You can make an organized list to show all possible outcomes. Example 1 Continued

10-3 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. Example 1 Continued BG RG BB RB BR RR Bag 2Bag 1

10-3 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. Example 1 - A DIFFERENT PLAN Combinations From 2 nd bag Pick from FIRST bag RRRRBRB Combinations From 2 nd bag Pick from FIRST bag BRBRBBB Combinations From 2 nd bag Pick from FIRST bag GRGRBGB

10-3 Sample Spaces Look Back 4 Each possible outcome that is recorded in the list is different. Example 1 Continued

10-3 Sample Spaces PRACTICE 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?

10-3 Sample Spaces Practice 1 Continued 1 Understand the Problem Rewrite the question as a statement. Find all the possible outcomes of drawing one marble from each bag, and determine the size of the sample space. List the important information. There are two bags. The other bag has a blue and a red marble. One bag has a green marble and a red marble.

10-3 Sample Spaces Practice 1 Continued 2 Make a Plan You can make an organized list to show all possible outcomes.

10-3 Sample Spaces Practice 1 Continued Solve 3 Let R = red marble, B = blue marble, and G = green marble. Record each possible outcome. RR BR RG BG Bag 2Bag 1 The four possible outcomes are GB, GR, RB, and RR. There are four possible outcomes in the sample space.

10-3 Sample Spaces Practice 1 Continued Look Back 4 Each possible outcome that is recorded in the list is different.

10-3 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? Example 2: Using a Tree Diagram to Find a Sample Space Make a tree diagram to show the sample space.

10-3 Sample Spaces 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.

10-3 Sample Spaces Practice 2 There are 2 marbles and 3 cubes in a board game. The marbles are pink and green. The cubes are numbered 1, 2, and 3. A player randomly selects one marble and one cube. What are all the possible outcomes? How outcomes are in the sample space? Make a tree diagram to show the sample space.

10-3 Sample Spaces Practice 2 Continued List each number of 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.

10-3 Sample Spaces In Example 1, there are three outcomes for the first bag and two outcomes for the second bag. In Example 2, there are four outcomes for the cards and two outcomes for the tiles. Cards Tiles First bagSecond bag

10-3 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.

10-3 Sample Spaces Carrie rolls two 1–6 number cubes. How many outcomes are possible? 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.

10-3 Sample Spaces Practice 3 Sammy picks three 1-5 number cubes from a bag. After she picks a number cube, she puts in back in the bag. How many outcomes are possible ? List the number of outcomes for each separate experiment. Number of ways the first cube can be picked: 5 Number of ways the second cube can be picked: 5 5 · 5 · 5 = 125 There are 125 possible outcomes when Sammy rolls number cubes. Use the Fundamental Counting Principle. Number of ways the third cube can be picked: 5

10-3 Sample Spaces Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

10-3 Sample Spaces Lesson Quiz What are all the possible outcomes? How many outcomes are in the sample space? 1. a three question true-false test 2. tossing four coins 3. choosing a pair of co-captains from the following athletes: Anna, Ben, Carol, Dan, Ed, Fran

10-3 Sample Spaces Lesson Quiz What are all the possible outcomes? How many outcomes are in the sample space? 1. a three question true-false test 2. tossing four coins 3. choosing a pair of co-captains from the following athletes: Anna, Ben, Carol, Dan, Ed, Fran 8 possible outcomes: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF 16 possible outcomes: HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT 15 possible outcomes: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF

10-3 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

10-3 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

10-3 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

10-3 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

10-3 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

10-3 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