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9-1 Probability
Pledge & Moment of Silence

Pre-Algebra
9-1 Probability
Pre-Algebra HOMEWORK
Page 449 #1-8
&
Page 453 #1-6
Pre-Algebra
Our Learning Goal
Students will be able to find theoretical
probabilities, including dependent and
independent events; estimate probabilities
using experiments and simulations; use
The Fundamental Counting Principle,
permutations, and combinations; and
convert between probability and odds of a
specified outcome.
Our Learning Goal Assignments
• Learn to find he probability of an event by using the definition of
probability (9-1)
• Learn to estimate probability using experimental methods (9-2)
9-1 Probability
Student Learning Goal Chart
Pre-Algebra
9-1 Probability
FAST TRACK!
9-1 AND 9-2
Pre-Algebra
9-1 Probability
Today’s Learning Goal Assignment
Learn to find the
probability of an
event by using the
definition of
probability.
Pre-Algebra
9-1 Probability
Lesson Quiz
Use the table to find the probability of each
event.
1. 1 or 2 occurring 0.351
2. 3 not occurring 0.874
3. 2, 3, or 4 occurring
0.794
Pre-Algebra
9-2 Experimental Probability
Today’s Learning Goal Assignment
Learn to estimate
probability using
experimental
methods.
9-2 Experimental Probability
Lesson Quiz: Part 1
1. Of 425, 234 seniors were enrolled in a math
course. Estimate the probability that a
randomly selected senior is enrolled in a
math course. 0.55, or 55%
2. Mason made a hit 34 out of his last 125
times at bat. Estimate the probability that he
will make a hit his next time at bat.
0.27, or 27%
9-2 Experimental Probability
Lesson Quiz: Part 2
3. Christina polled 176 students about their
favorite ice cream flavor. 63 students’ favorite
flavor is vanilla and 40 students’ favorite
flavor is strawberry. Compare the probability
of a student’s liking vanilla to a student’s
liking strawberry.
about 36% to about 23%
9-1 Probability
Vocabulary
experiment
trial
outcome
sample space
event
probability
impossible
certain
Pre-Algebra
9-1 Probability
An experiment is an activity in which results
are observed. Each observation is called a trial,
and each result is called an outcome. The
sample space is the set of all possible
outcomes of an experiment.
Experiment
Sample Space
flipping a coin
heads, tails
rolling a number cube
1, 2, 3, 4, 5, 6
guessing the number of
jelly beans in a jar
whole numbers
Pre-Algebra
9-1 Probability
An event is any set of one or more outcomes.
The probability of an event, written P(event),
is a number from 0 (or 0%) to 1 (or 100%) that
tells you how likely the event is to happen.
• A probability of 0 means the event is
impossible, or can never happen.
• A probability of 1 means the event is certain,
or has to happen.
• The probabilities of all the outcomes in the
sample space add up to 1.
Pre-Algebra
9-1 Probability
Never
happens
Happens about
half the time
Always
happens
1
2
3
4
1
0
1
4
0.25
0.5
0.75
1
0%
25%
50%
75%
100%
0
Pre-Algebra
9-1 Probability
Additional Example 1A: Finding Probabilities of
Outcomes in a Sample Space
Give the probability for each outcome.
A. The basketball team
has a 70% chance of
winning.
The probability of winning is P(win) =
70% = 0.7. The probabilities must add to
1, so the probability of not winning is
P(lose) = 1 – 0.7 = 0.3, or 30%.
Pre-Algebra
9-1 Probability
Try This: Example 1A
Give the probability for each outcome.
A. The polo team
has a 50%
chance of
winning.
The probability of winning is P(win) =
50% = 0.5. The probabilities must add to
1, so the probability of not winning is
P(lose) = 1 – 0.5 = 0.5, or 50%.
Pre-Algebra
9-1 Probability
Additional Example 1B: Finding Probabilities of
Outcomes in a Sample Space
Give the probability for each outcome.
B.
Three of the eight sections of the spinner are
labeled 1, so a reasonable estimate of the
probability that the spinner will land on 1 is
3
P(1) = .
8
Pre-Algebra
9-1 Probability
Additional Example 1B Continued
Three of the eight sections of the spinner are
labeled 2, so a reasonable estimate of the
probability that the spinner will land on 2 is
P(2) = 3 .
8
Two of the eight sections of the spinner are
labeled 3, so a reasonable estimate of the
probability that the spinner will land on 3 is
P(3) = 2 = 1 .
8 4
Check The probabilities of all the outcomes
must add to 1.
3 3
2
+ +
= 1
8 8
8
Pre-Algebra
9-1 Probability
Try This: Example 1B
Give the probability for each outcome.
B. Rolling a
number
cube.
Outcome
1
2
3
4
5
Probability
One of the six sides of a cube is labeled 1,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(1) = 1 .
6
One of the six sides of a cube is labeled 2,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(2) = 1 .
6
Pre-Algebra
6
9-1 Probability
Try This: Example 1B Continued
One of the six sides of a cube is labeled 3,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(3) = 1 .
6
One of the six sides of a cube is labeled 4,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(4) = 1 .
6
One of the six sides of a cube is labeled 5,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(5) = 1 .
6
Pre-Algebra
9-1 Probability
Try This: Example 1B Continued
One of the six sides of a cube is labeled 6,
so a reasonable estimate of the probability that
the spinner will land on 1 is P(6) = 1 .
6
Check The probabilities of all the outcomes
must add to 1.
1 1 1 1 1 1
+ + + + + =1
6 6 6 6 6 6
Pre-Algebra
9-1 Probability
To find the probability of an event, add the
probabilities of all the outcomes included in the
event.
Pre-Algebra
9-1 Probability
Additional Example 2A: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
A. What is the probability of not guessing 3 or
more correct?
The event “not three or more correct” consists of
the outcomes 0, 1, and 2.
P(not 3 or more) = 0.031 + 0.156 + 0.313 =
0.5, or 50%.
Pre-Algebra
9-1 Probability
Try This: Example 2A
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
A. What is the probability of guessing 3 or more
correct?
The event “three or more correct” consists of the
outcomes 3, 4, and 5.
P(3 or more) = 0.313 + 0.156 + 0.031 = 0.5,
or 50%.
Pre-Algebra
9-1 Probability
Additional Example 2B: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
B. What is the probability of guessing between 2
and 5?
The event “between 2 and 5” consists of the
outcomes 3 and 4.
P(between 2 and 5) = 0.313 + 0.156 = 0.469,
or 46.9%
Pre-Algebra
9-1 Probability
Try This: Example 2B
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
B. What is the probability of guessing fewer than
3 correct?
The event “fewer than 3” consists of the outcomes
0, 1, and 2.
P(fewer than 3) = 0.031 + 0.156 + 0.313 =
0.5, or 50%
Pre-Algebra
9-1 Probability
Additional Example 2C: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
C. What is the probability of guessing an even
number of questions correctly (not counting
zero)?
The event “even number correct” consists of the
outcomes 2 and 4.
P(even number correct) = 0.313 + 0.156 =
0.469, or 46.9%
Pre-Algebra
9-1 Probability
Try This: Example 2C
A quiz contains 5 true or false questions. Suppose
you guess randomly on every question. The table
below gives the probability of each score.
C. What is the probability of passing the quiz
(getting 4 or 5 correct) by guessing?
The event “passing the quiz” consists of the
outcomes 4 and 5.
P(passing the quiz) = 0.156 + 0.031 = 0.187, or
18.7%
Pre-Algebra
9-1 Probability
Additional Example 3: Problem Solving Application
Six students are in a race. Ken’s
probability of winning is 0.2. Lee is
twice as likely to win as Ken. Roy is 1
4
as likely to win as Lee. Tracy, James,
and Kadeem all have the same
chance of winning. Create a table of
probabilities for the sample space.
Pre-Algebra
9-1 Probability
Additional Example 3 Continued
1
Understand the Problem
The answer will be a table of probabilities.
Each probability will be a number from 0 to
1. The probabilities of all outcomes add to 1.
List the important information:
• P(Ken) = 0.2
• P(Lee) = 2  P(Ken) = 2  0.2 = 0.4
1 
1
• P(Roy) = 4 P(Lee) = 4 0.4 = 0.1
• P(Tracy) = P(James) = P(Kadeem)
Pre-Algebra
9-1 Probability
Additional Example 3 Continued
2
Make a Plan
You know the probabilities add to 1, so
use the strategy write an equation. Let
p represent the probability for Tracy,
James, and Kadeem.
P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1
0.2 + 0.4
+ 0.1
+
p
+
p
+
p
=1
0.7 + 3p = 1
Pre-Algebra
9-1 Probability
Additional Example 3 Continued
3
Solve
0.7 + 3p = 1
–0.7
–0.7
Subtract 0.7 from both sides.
3p = 0.3
3p = 0.3
3
3
p = 0.1
Pre-Algebra
Divide both sides by 3.
9-1 Probability
Additional Example 3 Continued
4
Look Back
Check that the probabilities add to 1.
0.2 + 0.4 + 0.1 + 0.1 + 0.1 + 0.1 = 1 
Pre-Algebra
9-1 Probability
Try This: Example 3
Four students are in the Spelling Bee.
Fred’s probability of winning is 0.6.
Willa’s chances are one-third of Fred’s.
Betty’s and Barrie’s chances are the
same. Create a table of probabilities
for the sample space.
Pre-Algebra
9-1 Probability
Try This: Example 3 Continued
1
Understand the Problem
The answer will be a table of probabilities.
Each probability will be a number from 0 to
1. The probabilities of all outcomes add to 1.
List the important information:
• P(Fred) = 0.6
1
1
• P(Willa) = 3 P(Fred) = 3 0.6 = 0.2
• P(Betty) = P(Barrie)
Pre-Algebra
9-1 Probability
Try This: Example 3 Continued
2
Make a Plan
You know the probabilities add to 1, so use
the strategy write an equation. Let p
represent the probability for Betty and
Barrie.
P(Fred) + P(Willa) + P(Betty) + P(Barrie) = 1
0.6
+
0.2
+
p
+
p
=1
0.8 + 2p = 1
Pre-Algebra
9-1 Probability
Try This: Example 3 Continued
3
Solve
0.8 + 2p = 1
–0.8
–0.8
Subtract 0.8 from both sides.
2p = 0.2
p = 0.1
Outcome
Fred
Willa
Betty
Barrie
Probability
0.6
0.2
0.1
0.1
Pre-Algebra
9-1 Probability
Try This: Example 3 Continued
4
Look Back
Check that the probabilities add to 1.
0.6 + 0.2 + 0.1 + 0.1 = 1 
Pre-Algebra
9-1 Probability
Lesson Quiz
Use the table to find the probability of each
event.
1. 1 or 2 occurring 0.351
2. 3 not occurring 0.874
3. 2, 3, or 4 occurring
0.794
Pre-Algebra
9-1
9-2 Probability
Experimental Probability
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
9-2 Experimental Probability
Warm Up
Use the table to find the probability of
each event.
1. A or B occurring 0.494
2. C not occurring 0.742
3. A, D, or E occurring
0.588
Pre-Algebra
Problem of the Day
A spinner has 4 colors: red, blue, yellow,
and green. The green and yellow
sections are equal in size. If the
probability of not spinning red or blue is
40%, what is the probability of spinning
green? 20%
Today’s Learning Goal Assignment
Learn to estimate
probability using
experimental
methods.
Vocabulary
experimental probability
In experimental probability, the likelihood
of an event is estimated by repeating an
experiment many times and observing the
number of times the event happens. That
number is divided by the total number of
trials. The more the experiment is repeated,
the more accurate the estimate is likely to
be.
probability 
number of times the event occurs
total number of trials
Additional Example 1A: Estimating the Probability of
an Event
A. The table shows the results of 500 spins of
a spinner. Estimate the probability of the
spinner landing on 2.
probability  number of spins that landed on 2 = 186
total number of spins
500
The probability of landing on 2 is about 0.372, or 37.2%.
Try This: Example 1A
A. Jeff tosses a quarter 1000 times and finds
that it lands heads 523 times. What is the
probability that the next toss will land
heads? Tails?
523
P(heads) = 1000= 0.523
P(heads) + P(tails) = 1
0.523 + P(tails) = 1
The probabilities must
equal 1.
P(tails) = 0.477
Additional Example 1B: Estimating the Probability of
an Event
B. A customs officer at the New York–Canada
border noticed that of the 60 cars that he saw,
28 had New York license plates, 21 had
Canadian license plates, and 11 had other
license plates. Estimate the probability that a
car will have Canadian license plates.
probability  number of Canadian license plates
total number of license plates
= 21
60
= 0.35
The probability that a car will have Canadian license
plates is about 0.35, or 35%.
Try This: Example 1B
B. Josie sells TVs. On Monday she sold 13
plasma displays and 37 tube TVs. What is the
probability that the first TV sold on Tuesday
will be a plasma display? A tube TV?
probability ≈ number of plasma displays = 13
= 13
total number of TVs
13 + 37 50
P(plasma) = 0.26
P(plasma) + P(tube) = 1
0.26
+ P(tube) = 1
P(tube) = 0.74
Additional Example 2: Application
Use the table to compare the probability
that the Huskies will win their next game
with the probability that the Knights will
win their next game.
Additional Example 2 Continued
probability 
number of wins
total number of games
probability for a Huskies win  79  0.572
138
probability for a Knights win  90  0.616
146
The Knights are more likely to win their next
game than the Huskies.
Try This: Example 2
Use the table to compare the probability
that the Huskies will win their next game
with the probability that the Cougars will
win their next game.
Try This: Example 2 Continued
probability 
number of wins
total number of games
probability for a Huskies win  79  0.572
138
probability for a Cougars win  85  0.567
150
The Huskies are more likely to win their next
game than the Cougars.
Lesson Quiz: Part 1
1. Of 425, 234 seniors were enrolled in a math
course. Estimate the probability that a
randomly selected senior is enrolled in a
math course. 0.55, or 55%
2. Mason made a hit 34 out of his last 125
times at bat. Estimate the probability that he
will make a hit his next time at bat.
0.27, or 27%
Lesson Quiz: Part 2
3. Christina polled 176 students about their
favorite ice cream flavor. 63 students’ favorite
flavor is vanilla and 40 students’ favorite
flavor is strawberry. Compare the probability
of a student’s liking vanilla to a student’s
liking strawberry.
about 36% to about 23%