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Sample Space and Outcomes
Outcome – possible results of an action
Sample Space – the set of all possible outcomes
Tree diagram – organized way to represent a
sample space
Outcome is the predicted result of an event
1. Roll a die – outcomes (1,2,3,4,5,6)
2. Spin this spinner
Outcomes – ( Red,
Orange , purple,
yellow, green)
3. Toss a coin – outcomes (heads, tails)
For the experiment to be fair or equally likely, the outcome has to
be the same size
Experiment
flipping a coin
Sample Space
heads, tails
rolling a number cube
1, 2, 3, 4, 5, 6
guessing the number
of marbles in a jar
whole numbers
A tree diagram is used to organize the list of all possible
outcomes.
Use a tree diagram to list the possible outcomes, if you
toss a penny and spin a spinner.
EX1)
2 outcomes
4 outcomes
H
Step 1 Set up the first
T
H
You should have 8
outcomes because
2X4=8
outcome horizontally.
(Spaced out for room.)
Step 2 Branch off the same
R Y
B
G
HY HB HG
G
number of outcomes
for the second event
TR TY TB TG
Step 3 Label each branch using
R Y
B
the second outcome
Step 4 List outcomes
EX2) List the possible outcomes if you spin a spinner twice.
4 outcomes
4 outcomes
How many outcome should be in the list? 4 X 4 = 16 outcomes
First Spin
Second Spin
Outcomes
16
R
R
Y B
RR
RY
RB
RG
Y
G
R Y B G
YR
YY
YB
YG
G
R Y B G
GR
GY
GB
GG
B
R Y
BR
BY
BB
BG
B G
Ex3) You can use a grid instead of tree if the sample space will be large.
Rolling two dice. Outcomes = 36
1
1
2
3
4
5
6
1,1
2,1
3,1
4,1
5,1
6,1
2
1,2
2,2
3,2
4,2
5,2
6,2
3
4
5
6
1,3 1,4 1,5 1,6
2,3 2,4 2,5 2,6
3,3 3,4 3,5 3,6
4,3 4,4 4,5 4,6
5,3 5,4 5,5 5,6
6,3 6,4 6,5 6,6
Essential Question
What multiple representations help determine the
number of outcomes for an action?
Assignment
With your partner
Page 365 and 366
Date ________________________
Sample Space and Outcomes
Outcome – possible results of an action
Sample Space – the set of all possible outcomes
Tree diagram – organized way to represent a
sample space
Outcome is the predicted result of an event
1. Roll a die –
2. Spin this spinner
3. Toss a coin
For the experiment to be fair or equally likely, the outcome has to
be the same size
Experiment
Sample Space
flipping a coin

rolling a number cube

guessing the number
of marbles in a jar

A tree diagram is used to organize the list of all possible
outcomes.
EX1)
Use a tree diagram to list the possible outcomes, when
you toss a penny and spin a spinner.
2 outcomes
__
4 outcomes
__
Step 1 Set up the first
outcome __________
Step 2 Branch off the same
__________________
for the second event
Step 3 ______ each branch using
the __________ outcome
Step 4 List outcomes
EX2) List the possible outcomes if you spin a spinner twice.
How many outcome should be in the list?
First Spin
Second Spin
Ex3) You can use a grid instead of tree if the sample space will be large.
Rolling two dice. Outcomes =
1
1
2
3
4
5
6
2
3
4
5
6
Essential Question
What multiple representations help determine the
number of outcomes for an action?