5Warm Up1. 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?4723
6CaliforniaStandardsSDAP3.1 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
7Objective: You will learn how to (YWLHT) use counting methods to determine possible outcomes. 7777
9Together, 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.
10Example 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?
11Example 1 ContinuedLet R = red tile, B = blue tile, and G = green tile.Bag 1Bag 2RBGRecord each possible outcome.RR: 2 red tilesRB: 1 red, 1 blue tileBR: 1 blue, 1 red tileBB: 2 blue tilesGR: 1 green, 1 red tileGB: 1 green, 1 blue tile
12Example 1 ContinuedFind the probability of each outcome.P(2 red tiles) =16Bag 1Bag 2RBGP(1 red, 1 blue tile) =13P(2 blue tiles) =16P(1 green, 1 red tile) =16P(1 green, 1 blue tile) =16
13Check It Out! Example 2Darren 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?
14Check It Out! Example 2 Continued Let R = red marble, B = blue marble, andG = green marble.Bag 1Bag 2GBRRecord each possible outcome.GB: 1 green, 1 blue marbleGR: 1 green, 1 red marbleRB: 1 red, 1 blue marbleRR: 2 red marbles
15Check It Out! Example 2 Continued Find the probability of each outcome.P(1 green, 1 blue marble) =14Bag 1Bag 2GBRP(1 green, 1 red marble) =14P(1 red, 1 blue marble) =14P(2 red marbles) =14
16When the number of possible outcomes of an experiment increases, it may be easier to track all the possible outcomes on a tree diagram.
17Example 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?
18List each letter on the cards. Then list each number on the tiles. Example 3 ContinuedList each letter on the cards. Then list each numberon the tiles.NSEW1 21 21 21 2N N2S S2E E2W1 W2There are eight possible outcomes in the sample space.P(E and 2 card) =number of ways the event can occurtotal number of equally likely outcomes18=The probability that the player will select the E and 2 card is .18
19Check It Out! Example 4There 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.
20Check It Out! Example 4 Continued List each number on the cubes. Then list each colorof the marbles.123Pink GreenPink GreenPink Green1P G2P G3P GThere are six possible outcomes in the sample space.P(1 and green) =number of ways the event can occurtotal number of equally likely outcomes16=The probability that the player will select the cube numbered 1and the green marble is .16
21The 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.
22Example 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 outcomesUse the Fundamental Counting Principle.6 · 6 = 36There are 36 possible outcomes when Carrie rollstwo number cubes.
23Check It Out! Example 6A 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 = 9There are 9 possible outcomes for sandwiches.
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252. a three question true-false test Lesson Quiz1. 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 test3. choosing a pair of co-captains from the following athletes: Anna, Ben, Carol, Dan, Ed, Fran1 8HHH, HHT, HTH, HTT, THH, THT, TTH, TTT;8 possible outcomes: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF15 possible outcomes: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF