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Preview Warm Up California Standards Lesson Presentation

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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? 4 7 2 3

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California Standards 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

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**Objective: You will learn how to (YWLHT) use counting methods to determine possible outcomes.**

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Vocabulary sample space compound event Fundamental Counting Principle

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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.

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**Example 1: Using a Table to Find a Sample Space**

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?

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Example 1 Continued Let R = red tile, B = blue tile, and G = green tile. Bag 1 Bag 2 R B G Record each possible outcome. 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

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Example 1 Continued Find the probability of each outcome. P(2 red tiles) = 1 6 Bag 1 Bag 2 R B G P(1 red, 1 blue tile) = 1 3 P(2 blue tiles) = 1 6 P(1 green, 1 red tile) = 1 6 P(1 green, 1 blue tile) = 1 6

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Check It Out! Example 2 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?

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**Check It Out! Example 2 Continued**

Let R = red marble, B = blue marble, and G = green marble. Bag 1 Bag 2 G B R Record each possible outcome. GB: 1 green, 1 blue marble GR: 1 green, 1 red marble RB: 1 red, 1 blue marble RR: 2 red marbles

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**Check It Out! Example 2 Continued**

Find the probability of each outcome. P(1 green, 1 blue marble) = 1 4 Bag 1 Bag 2 G B R P(1 green, 1 red marble) = 1 4 P(1 red, 1 blue marble) = 1 4 P(2 red marbles) = 1 4

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When the number of possible outcomes of an experiment increases, it may be easier to track all the possible outcomes on a tree diagram.

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**Example 3: 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. 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?

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**List each letter on the cards. Then list each number on the tiles.**

Example 3 Continued List each letter on the cards. Then list each number on the tiles. N S E W 1 2 1 2 1 2 1 2 N N2 S S2 E E2 W1 W2 There are eight possible outcomes in the sample space. P(E and 2 card) = number of ways the event can occur total number of equally likely outcomes 1 8 = The probability that the player will select the E and 2 card is . 1 8

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Check It Out! Example 4 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.

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**Check It Out! Example 4 Continued**

List each number on the cubes. Then list each color of the marbles. 1 2 3 Pink Green Pink Green Pink Green 1P G 2P G 3P G There are six possible outcomes in the sample space. P(1 and green) = number of ways the event can occur total number of equally likely outcomes 1 6 = The probability that the player will select the cube numbered 1 and the green marble is . 1 6

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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.

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**Example 5: Recreation Application**

Carrie rolls two 1–6 number cubes. How many outcomes are possible? The first number cube has 6 outcomes. List the number of outcomes for each simple event. The second number cube has 6 outcomes Use the Fundamental Counting Principle. 6 · 6 = 36 There are 36 possible outcomes when Carrie rolls two number cubes.

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Check It Out! Example 6 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. List the number of outcomes for each simple event. There are 3 choices for meat. Use the Fundamental Counting Principle. 3 · 3 = 9 There are 9 possible outcomes for sandwiches.

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**Click to view Lesson Videos**

Home Learning Click to view Lesson Videos 24 24 24 24

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**2. a three question true-false test**

Lesson Quiz 1. Ian tosses 3 pennies. Use a tree diagram to find all the possible outcomes. What is the probability that all 3 pennies will land heads up? What are all the possible outcomes? How many outcomes are in the sample space? 2. a three question true-false test 3. choosing a pair of co-captains from the following athletes: Anna, Ben, Carol, Dan, Ed, Fran 1 8 HHH, HHT, HTH, HTT, THH, THT, TTH, TTT; 8 possible outcomes: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF 15 possible outcomes: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF

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