What is the probability that
the spinner will land on blue?
In this lesson you will learn how
to calculate the probability of an
event by creating a ratio.
Let’s Review
Ratios can be used to represent fractions
of an area or of a set.
A Common Mistake
Every event must have an equal probability
of occurring.
Core Lesson
Probability is the likelihood that an event
will take place.
Core Lesson
What is the probability that the spinner
will land on blue?
1
8
2
3
7 6
4
5
Core Lesson
Samuel has a bowl of fruit containing 3
apples, 2 oranges and 5 pears. If he
randomly picks 1 piece of fruit from the
bowl, what is the probability it will be a
pear or an apple?
Core Lesson
3 apples
2 oranges
+
5 pears
10 fruits total
In this lesson you have learned
how to calculate the probability
of an event by creating a ratio.
Guided Practice
When you roll a number cube with faces
numbered 1, 2, 3, 4, 5, 6, what is the
probability it will land on an odd number?
Quick Quiz
1
2
A bag has 40 blue chips and 60 green
chips. What is the probability that you
will randomly pick a blue chip from the
bag?
A bag has 4 blue marbles, 5 red marbles
and 6 green marbles. What is the
probability of picking a red or blue
marble?
Lesson 2
In this lesson you will learn how to
describe the probability of an event
by using a number line.
Core Lesson
The probability continuum:
l
impossible
l
certain
Core Lesson
The probability continuum:
l
impossible
0
l
certain
1
Core Lesson
The probability continuum:
l
l
l
l
l
1
0
impossible
certain
unlikely
equally likely
likely
Core Lesson
Core Lesson
The probability continuum:
l
l
l
l
l
1
0
impossible
certain
unlikely
equally likely
likely
Core Lesson
Core Lesson
The probability continuum:
l
l
l
l
l
1
0
impossible
certain
unlikely
equally likely
likely
In this lesson you have learned
how to describe the probability of
an event by using a number line.
Guided Practice
There are 12 pairs of socks in Flora’s
drawer, 9 are red, 2 are blue and 1 is
green. She takes out one pair of socks
without looking at the color. Describe (in
words) the likelihood of Flora picking out a
pair of red socks.
Extension Activities
A container contains 2 blue, 1 green, and 4
orange and 5 yellow marbles. Find the
probability of picking each marble and then
put the probabilities in order from unlikely
to likely chance of occurring.
Lesson 3
How can you use the
theoretical probability to
predict the results from an
experiment?
If you were to roll a six-sided die 600
times how many times would you predict
you would roll a 3 or 6?
In this lesson you will learn how
to predict the frequency of an
event by using the theoretical
probability.
Core Lesson
If you were to roll a six-sided die 600
times how many times would you predict
you would roll a 3 or 6?
Core Lesson
If you were to roll a six-sided die 600
times how many times would you predict
you would roll a 3 or 6?
In this lesson you have learned
how to predict the frequency of
an event by using the theoretical
probability.
Guided Practice
If you were to spin 400 times, predict how
many times you would land on blue?
Quick Quiz
A bag has 4 blue marbles, 6 green and 2
red. Marcus will pick a marble from the
bag and return it 60 times. Of the 60
times predict how many times you would
expect Marcus to pick a blue marble?
Quick Quiz
If you were to roll a six-sided die 150
times. How many times would you expect
to roll a number greater than 4?
Lesson 4
How do you find the experimental probability of
rolling a 7 based off the table below?
Trial
1
2
3
4
5
Sum
5
3
7
9
7
Trial
6
7
8
9
10
Sum
8
6
7
5
9
In this lesson you will learn how
to interpret a set of data by
comparing experimental and
theoretical probability.
Let’s Review
Experimental Probability:
Core Lesson
Trial
6
1
2
7
3
8
4
9
10
5
Sum
5
8
3
6
7
9
5
7
9
Trial ofSum
Number
times
6 a 7 was
8
rolled:
7
8 2
1
3
9
10
6
7
5
9
Core Lesson
1+1
2
1+2
3
1+3
4
2+1
3 2+2
4
5
2+3
5
1+4
6
1+5
1+6
7
8
7 2+6
6 2+5
2+4
4
6
3+4
7
8 3+6
3+1
5 3+3
3+2
9
3+5
4+1
5 4+2
9 4+6
7 4+4
6 4+3
8 4+5
10
5+1
8 5+4
6
10 5+6
5+3
9 5+5
11
5+2
7
6+1
7
6+2
8 6+3
9
6+4
11
10 6+5
6+6
12
In this lesson you have learned
how to interpret a set of data by
comparing experimental and
theoretical probability.
Guided Practice
Results from rolling a six-sided die:
# of
What is the experimental
Rolled
probability of rolling a 4?
times
How does that compare to
1
6
the theoretical probability?
2
15
3
18
4
11
5
3
6
7
Quick Quiz
After 60 spins, Chris had the following B A
A
C
results:
C
A
What is the
B B
Lette
#
experimental probability
of spinning a “B”? How
A
29
does that compare to
B
16
the theoretical
probability?
C
15
Quick Quiz
In a survey, Scott asked 50 people if they voted
for the current mayor. He recorded the results
in this table:
Yes
22
No
20
Private
3
Based on the survey, what is the probability that
the next person will say “No”?
A. 5%
B. 20%
C. 40%
D. 67%
Lesson 5
Scored
Missed
20
1
2
51
Score!
Miss!
Score!
How do you find the
experimental probability of him
making his next throw?
In this lesson you will learn how
to find the experimental
probability by creating a ratio.
Let’s Review
Core Lesson
Theoretical Probability:
Core Lesson
Experimental Probability:
3 times
10 trials
Core Lesson
Scored
Missed
20
5
In this lesson you have learned
how to find the experimental
probability by creating a ratio.
Guided Practice
After 50 spins, Chris landed on green 22
times. What is the experimental
probability of landing on green? How does
it compare to the theoretical probability?
Quick Quiz
A company manufactures CD players. The
quality control department checks 600 CD
players and discovers that 12 of them are
defective. What is the probability that a
CD player is not defective?
Quick Quiz
The ticket salesperson at the fair noticed
that 12 of the first 40 people buying
tickets paid with a credit card. What is
the experimental probability that the
next customer to buy a ticket will pay
with a credit card?
How can you use survey results
to make predictions for a whole
population?
For example, in a school of 300, Chris
surveyed 80 students and found that 44
students prefer chocolate ice cream.
Lesson 6
In this lesson you will learn how
to predict the frequency of an
event by using the results from
experiments.
Core Lesson
In a school of 300, Chris surveyed 80
students and found that 44 students
prefer chocolate ice cream.
Core Lesson
According to the survey results, we can predict
that 165 students at Chris’ school prefer
chocolate ice cream.
Core Lesson
To predict frequencies of an event using
the experimental probability:
In this lesson you have learned
how to predict the frequency of
an event by using the results
from experiments.
Guided Practice
Karen spun a spinner 50 times and recorded her
results in the table below. The spinner had five
numbered sections.
Section
Frequency
1
2
3
4
5
13
2
10
12
7
Based on the results in the
table, how many times should
Karen expect the spinner to
land on section 3 or 4 if she
spins the spinner 300 times?
Extension Activities
Have students do an experiment in which they
roll a die 25 times. Then have them use their
experimental probabilities to find how many
times they would expect a 1, 2, 3, etc.. If they
were to roll 100 or 1,000 more times.
Quick Quiz
The mayor of a town conducted an opinion survey
of 90 randomly selected voters. The mayor
wants to determine if a new shopping mall should
be built in town. The survey results are shown
below.
There are 1,440 voters
in town. How many
voters would be
expected to want the
new shopping mall built?
Want a new mall
60
Do Not Want a
New Mall
20
No Opinion
10
Quick Quiz
The spinner below is spun 20 times. The table
shows the results.
Section
Frequency
1
5
2
8
3
2
4
5
Based on these results, how many times would 2
be expected to appear in 60 spins?
Lesson 7
How do you determine the
sample space for rolling a sixsided die?
In this lesson you will learn how
to analyze the probability of an
event by assigning equal
probability to all outcomes.
Core Lesson
Sample space: set of all possible outcomes
in an experiment.
Core Lesson
+
+
+
+
{1, 2,P(4)=
3, 4, 5, 6}
+
=1
Core Lesson
+ +
+
+
+
+
+ + =1
=1
In this lesson you have learned
how to analyze the probability of
an event by assigning equal
probability to all outcomes.
Guided Practice
Using the spinner below, what is the sample
space? What is the probability that the spinner
will land on “B” as a percentage?
A
E
B
D
C
Quick Quiz
Mr. Smith’s class has 12 boys and 12 girls.
Mr. Smith will pick someone at random to
take attendance. What is the probability
that Jane, a girl, will be selected? What
is the probability of a girl?
Quick Quiz
A bag has only four marbles in it. One
blue, one green, one red and one yellow.
What is the sample space? What is the
probability of selecting a green marble?
How do you find the probability
A bag is full of 3 blue, 4 green and 2 red
of pulling a blue marble?
marbles.
In this lesson you will learn to
find the probability of events
with multiple possibilities by
combining their probabilities.
Let’s Review
Theoretical Probability:
1
8
2
7
3
6
4
5
A Common Mistake
Sample space:
A
C
{A, B, C}
B
A
C
{A, A, B, C, C}
Core Lesson
1
2 3 4
+
+
+
5 6 7
+
+
+
8
+
9
+
=1
Core Lesson
What is the probability of rolling a 4 or
greater?
+
+
+
+
P(≥4)=
{1, 2, 3, 4, 5, 6}
+
=1
In this lesson you have learned
how to find the probability of
events with multiple possibilities
by combining their probabilities.
Guided Practice
You roll a six-sided die. What is the
probability of rolling an odd number?
Quick Quiz
You roll a six-sided die. What is the
probability of rolling a 3 or greater?
Quick Quiz
What is the probability of spinning a 3 or
higher on the spinner below?
4
1
2
3
2
4
1
3
Lesson 8
How do you describe the
discrepancies in experimental
and theoretical probabilities ?
After 6 trials, Chris found that the
experimental probability for rolling a 4
was
.
In this lesson you will learn how
to explain discrepancies in results
from a probability model by
comparing experimental and
theoretical probabilities.
Core Lesson
After 6 trials, Chris found that the
experimental probability for rolling a 4
was
.
Core Lesson
Theoretical:
Experimental:
20
50
6 trials
Core Lesson
Sample space is too large.
In this lesson you have learned
how to explain discrepancies in
results from probability models
by comparing experimental and
theoretical probabilities.
Guided Practice
Compare the theoretical and experimental
probabilities of the spinner landing on green. Are
there any discrepancies? Why or why not?
Section
Frequency
Green
5
Orange
9
Red
3
Yellow
7
Blue
6
Quick Quiz
A bag has 4 blue marbles, 6 green marbles and 10
red marbles. A marble is picked at random and
then returned. After 50 pulls, 35 red marbles
were chosen. Is there a discrepancy between
the experimental and theoretical probabilities?
Why or why not?
Quick Quiz
The table below shows the results from 20
tosses of a fair coin.
Heads
Tails
11
9
Is there a discrepancy in the theoretical and
experimental probabilities of getting a tails?
Why or why not?