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Warm Up
California Standards
Lesson Presentation

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5. 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

6. 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

7. Objective: You will learn how to (YWLHT) use counting methods to determine possible outcomes.7 7 7 7

8. Vocabulary
sample space
compound event
Fundamental Counting Principle

9. 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.

10. 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?

11. 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

12. 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

13. 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?

14. 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

15. 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

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

17. 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?

18. 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

19. 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.

20. 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

21. 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.

22. 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.

23. 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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Home Learning
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25. 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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