8-4 Sample Spaces
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
8-4 Sample Spaces
Warm Up
1. A dog catches 8 out of 14 flying disks
4
thrown. What is the experimental
7
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? 2
3
Holt CA Course 1
8-4 Sample Spaces
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
Holt CA Course 1
8-4 Sample Spaces
Vocabulary
sample space
compound event
Fundamental Counting Principle
Holt CA Course 1
8-4 Sample Spaces
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.
Holt CA Course 1
8-4 Sample Spaces
Additional 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?
Holt CA Course 1
8-4 Sample Spaces
Additional Example 1 Continued
Let R = red tile, B = blue tile, and G = green tile.
Bag 1 Bag 2
R
R
Record each possible outcome.
RR: 2 red tiles
R
B
B
B
R
B
RB: 1 red, 1 blue tile
BR: 1 blue, 1 red tile
BB: 2 blue tiles
G
G
R
B
GR: 1 green, 1 red tile
GB: 1 green, 1 blue tile
Holt CA Course 1
8-4 Sample Spaces
Additional Example 1 Continued
Find the probability of each outcome.
Bag 1 Bag 2
R
R
R
B
B
B
R
B
G
G
R
B
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P(2 red tiles) = 1
6
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
8-4 Sample Spaces
Check It Out! Example 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. Use a
table to find all the possible outcomes.
What is the theoretical probability of each
outcome?
Holt CA Course 1
8-4 Sample Spaces
Check It Out! Example 1 Continued
Let R = red marble, B = blue marble, and
G = green marble.
Bag 1 Bag 2
G
B
G
R
R
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R
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
8-4 Sample Spaces
Check It Out! Example 1 Continued
Find the probability of each outcome.
Bag 1 Bag 2
G
B
G
R
R
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R
B
R
P(1 green, 1 blue marble) = 1
4
P(1 green, 1 red marble) = 1
4
P(1 red, 1 blue marble) = 1
4
P(2 red marbles) = 1
4
8-4 Sample Spaces
When the number of possible outcomes of
an experiment increases, it may be easier to
track all the possible outcomes on a tree
diagram.
Holt CA Course 1
8-4 Sample Spaces
Additional Example 2: 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?
Make a tree diagram to show the sample space.
Holt CA Course 1
8-4 Sample Spaces
Additional Example 2 Continued
List each letter on the cards. Then list each number
on the tiles.
S
N
1
N1
2
N2
1
S1
W
E
2
S2
1
E1
2
E2
1
W1
2
W2
There are eight possible outcomes in the sample space.
number of ways the event can occur
total number of equally likely outcomes
= 1
8
P(E and 2 card) =
1
The probability that the player will select the E and 2 card is 8 .
Holt CA Course 1
8-4 Sample Spaces
Check It Out! Example 2
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.
Holt CA Course 1
8-4 Sample Spaces
Check It Out! Example 2 Continued
List each number on the cubes. Then list each color
of the marbles.
1
Pink Green
1P
1G
2
3
Pink Green
2P
2G
Pink Green
3P
3G
There are six possible outcomes in the sample space.
number of ways the event can occur
P(1 and green) =
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
Holt CA Course 1
8-4 Sample Spaces
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.
Holt CA Course 1
8-4 Sample Spaces
Additional Example 3: Recreation Application
Carrie rolls two 1–6 number cubes. How many
outcomes are possible?
The first number cube
has 6 outcomes.
The second number cube
has 6 outcomes
List the number of
outcomes for each
simple event.
6 · 6 = 36
Use the Fundamental
Counting Principle.
There are 36 possible outcomes when Carrie rolls
two number cubes.
Holt CA Course 1
8-4 Sample Spaces
Check It Out! Example 3
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.
There are 3 choices for
meat.
List the number of
outcomes for each
simple event.
3·3=9
Use the Fundamental
Counting Principle.
There are 9 possible outcomes for sandwiches.
Holt CA Course 1
8-4 Sample Spaces
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?
1
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT; 8
What are all the possible outcomes? How
many outcomes are in the sample space?
2. a three question true-false test
8 possible outcomes: TTT, TTF, TFT, TFF, FTT, FTF, FFT,
FFF
3. choosing a pair of co-captains from the following
athletes: Anna, Ben, Carol, Dan, Ed, Fran
15 possible outcomes: AB, AC, AD, AE, AF, BC, BD, BE,
BF, CD, CE, CF, DE, DF, EF
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