Transcript over Lesson 9-3 - cloudfront.net

Lesson 9-1
Simple Events
Lesson 9-2
Sample Spaces
Lesson 9-3
The Fundamental Counting Principle
Lesson 9-4
Permutations
Lesson 9-5
Combinations
Lesson 9-6
Problem-Solving Investigation:
Act it Out
Lesson 9-7
Theoretical and Experimental
Probability
Lesson 9-8
Compound Events
Five-Minute Check (over Chapter 8)
Main Idea and Vocabulary
California Standards
Key Concept: Probability
Example 1: Find Probability
Example 2: Real-World Example
Example 3: Find a Complementary Event
• Find the probability of a simple event.
• outcome
• simple event
• probability
• random
• complementary event
Standard 6SDAP3.3 Represent probabilities
as ratios, proportions, decimals between 0 and 1,
and percentages between 0 and 100 and verify that
the probabilities computed are reasonable; know
that if P is the probability of an event, 1 – P is the
probability of an event not occurring.
•Definition: An outcome is any one of the possible
results of an action.
•Definition: A simple event is one outcome or a
collection of outcomes.
•Definition: Probability is the chance of an event
happening.
Find Probability
If the spinner shown below is spun once, what is
the probability of it landing on an odd number?
= 50%
What is the probability of rolling a number less than
three on a number cube marked with 1, 2, 3, 4, 5, and
6 on its faces?
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
GAMES A game requires spinning the spinner
shown below. If the number spun is greater than 3,
the player wins. What is the probability of winning
the game?
The possible outcomes of spinning the spinner are 1, 2,
3, and 4. In order to win, you would need to spin a 4.
=
The possible outcomes of spinning the spinner are 1, 2,
3, and 4. In order to win, you would need to spin a 4.
=
Answer:
BrainPOP:
Probability of Events
GAMES A game requires spinning the
spinner shown. If the number spun is
less than or equal to 2, the player wins.
What is the probability of winning the
game?
A.
B.
1.
2.
3.
4.
0%
C.
D. 1
A
B
C
D
A
B
C
D
Find a Complementary Event
GAMES A game requires spinning the
spinner shown. If the number spun is
greater than 3, the player wins. What is
the probability of not winning?
Definition of complementary
events
= 75%
Find a Complementary Event
Answer:
,
or 0.75, or 75%.
GAMES A game requires rolling a number cube
marked with 1, 2, 3, 4, 5, and 6 on its faces twice. If the
sum of the two rolls is five or less, the player wins.
What is the probability of not winning the game?
A.
B.
C.
0%
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
• Find sample spaces and probabilities.
• sample space
• tree diagram
• fair game
Find the Sample Space
CHILDREN A couple decided to have two children.
Find the sample space of the children’s genders if
having a boy is equally likely as having a girl.
Make a table that shows all of the possible outcomes.
Answer:
CARS A car dealership has a new model of
convertible. The convertible comes in both two and
four door in red, black, yellow, or orange. Find the
sample space for all possible styles of convertible a
customer may purchase.
A. 6
B. 4
C. 8
D. 12
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Amy was trying to decide what kind of sandwich to
make. She had two kinds of bread, wheat and
sourdough. And she had three kinds of lunchmeat: ham,
turkey, and roast beef. Which list shows all the possible
bread-lunchmeat combinations?
A
B
C
D
When purchasing a new car, Debbie has the choice of
black, silver, or blue for the exterior color and black,
gray, or tan for the interior color. How many possible
outcomes are in the sample space?
A. 3
0%
B. 6
C. 9
D. 12
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Find Probability
GAMES Peter and Linda are playing a game in
which the spinner below is spun twice. If the sum of
the numbers spun is even, Peter wins. If the sum of
the numbers is odd, Linda wins. Find the sample
space. Then determine whether the game is fair.
Answer: The game is not fair.
GAMES A game is played in which a number cube is
rolled twice. If the sum of the numbers rolled is
greater than seven, the player wins the game.
Determine whether this is a fair game.
A. yes
B. No, because the probability of
winning is greater than the
1.
A
probability of losing.
2.
B
C. No, because the probability of
3.
C
winning is less than the
4.
D
probability of losing.
D. not enough information to
answer
0%
A
B
C
D
Five-Minute Check (over Lesson 9-2)
Main Idea and Vocabulary
California Standards
Key Concept: Fundamental Counting Principle
Example 1: Find the Number of Outcomes
Example 2: Real-World Example
• Use multiplication to count outcomes and find
probabilities.
• Fundamental Counting Principle
Standard 6SDAP3.1 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.
Find the Number of Outcomes
Find the total number of outcomes when a number
from 0 to 9 is picked randomly and then a letter
from A to D is picked randomly.
number of
outcomes for
number
10
number of
outcomes for
letter
●
4
total number
of outcomes
=
Answer: There are 40 possible outcomes.
40
The school student council is electing one president,
one secretary, and one treasurer. There are four
students running for president, three running for
secretary, and five running for treasurer. Find the
number of ways the positions can be filled.
A. 12
B. 60
0%
D
A
0%
A
B
0%
C
D
C
D. 45
A.
B.
0%
C.
D.
B
C. 15
CLOTHING The table below shows the shirts, shorts,
and shoes in Gerry’s wardrobe. How many possible
outfits—one shirt, one pair of shorts, and one pair of
shoes—can he choose?
number of
shirts
4
Check
number of
shorts
●
3
total
number of
outfits
number of
shoes
●
2
=
24
You can check your work by drawing a tree
diagram and listing the 24 outcomes.
Answer: There are 24 possible outfits that Gerry can
choose.
SANDWICHES The table below shows the types of
bread, types of cheese, and types of meat that are
available to make a sandwich. How many possible
sandwiches can be made by selecting one type of
bread, one type of cheese, and one type of meat?
A. 3
B. 9
C. 18
D. 27
1.
2.
3.
4.
A
B
C
D
A
0%
B
C
D
Five-Minute Check (over Lesson 9-3)
Main Idea and Vocabulary
California Standards
Example 1: Find a Permutation
Example 2: Real-World Example: Find Probability
• Find the number of permutations of a set of objects
and find probabilities.
• permutation
Standard 6SDAP3.1 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.
Find a Permutation
BOWLING A team of bowlers has five members
who bowl one at a time. In how many orders can
they bowl?
Find the number of possible orders using the
Fundamental Counting Principle.
5 ● 4 ● 3 ● 2 ● 1 = 120
There are 5 choices for the 1st bowler, 4 choices for the
2nd bowler, 3 choices for the 3rd bowler, 2 choices for
the 4th bowler, and 1 choice for the 5th bowler.
Answer: There are 120 orders in which the five
members of the bowling team can bowl.
TRACK AND FIELD A relay team has four members
who run one at a time. In how many orders can they
run?
A. 1
B. 4
C. 16
D. 24
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Find Probability
RAFFLE A school fair holds a raffle with 1st, 2nd,
and 3rd prizes. Seven people enter the raffle,
including Marcos, Lilly, and Heather. What is the
probability that Marcos will win the 1st prize, Lilly
will win the 2nd prize, and Heather will win the 3rd
prize?
There are 7 choices for first place.
There are 6 choices for second place
and 5 for third.
7 ● 6 ● 5 = 210 ← The number of
permutations of 3 places
Find Probability
There are 210 possible arrangements, or permutations,
of the 2 places. Since there is only one way of
arranging Marcos, Lilly, and Heather in 1st, 2nd, and
3rd place respectively, the probability of this event
is
Answer:
CLUBS The president and vice-president of the
French Club will be randomly selected from a jar of
24 names. Find the probability that Sophie will be
selected as president and Peter selected as vicepresident.
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
Five-Minute Check (over Lesson 9-4)
Main Idea and Vocabulary
California Standards
Example 1: Find the Number of Combinations
Example 2: Real-World Example
Example 3: Real-World Example
• Find the number of combinations of a set of objects
and find probabilities.
• combination
Standard 6SDAP3.1 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.
Find the Number of Combinations
DECORATING Ada can select from seven paint
colors for her room. She wants to choose two
colors. How many different pairs of colors can she
choose?
Method 1 Make a list.
Number the colors 1 through 7.
1, 2
1, 5
2, 3
2, 6
3, 5
4, 5
5, 6
1, 3
1, 6
2, 4
2, 7
3, 6
4, 6
5, 7
1, 4
1, 7
2, 5
3, 4
3, 7
4, 7
6, 7
There are 21 different pairs of colors.
Find the Number of Combinations
Method 2 Use a permutation.
Step 1
Find the number of permutations of the
entire set.
Step 2
Step 3
7 ● 6 = 42
Find the number of ways to arrange the 2
colors.
2●1=2
Find the number of combinations.
Answer: There are 21 different pairs of colors Ada can
choose.
HOCKEY The Brownsville Badgers hockey team has
14 members. Two members of the team are to be
selected to be the team’s co-captains. How many
different pairs of players can be selected to be the
co-captains?
A. 2
B. 14
0%
D
A
B
0%
C
D
C
A
D. 182
0%
B
C. 91
A.
B.
0%
C.
D.
INTRODUCTIONS Ten managers attend a business
meeting. Each person exchanges names with each
other person once. How many introductions will
there be?
Find the number of ways 2 managers exchange names
from the group of 10.
There are 10 ● 9 or 90 ways to
choose 2 managers.
There are 2 ● 1 or 2 ways to
arrange 2 managers.
→
→
Check
Make a diagram in which each manager is
represented by a point. Draw line segments
between two points to represent the
introductions. There are 45 line segments.
Answer: There will be 45 introductions taking place.
INTRODUCTIONS If 15 managers attend a business
meeting, how many introductions will there be?
A. 15
B. 45
C. 85
D. 105
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
If the introductions in Example 2 are made at
random, what is the probability that Ms. Apple and
Mr. Zimmer will be the last managers to exchange
names?
Answer:
INTRODUCTIONS What is the probability that Ms.
Apple and Mr. Zimmer will be the last managers to
exchange names if there are 15 managers at the
business meeting?
A.
B.
C.
0%
1.
2.
3.
4.
A
D.
A
B
C
D
B
C
D
Five-Minute Check (over Lesson 9-5)
Main Idea
California Standards
Example 1: Act It Out
• Solve problems by acting it out.
Standard 6SDAP3.2 Use data to estimate the
probability of future events (e.g., batting averages or
number of accidents per mile driven).
Standard 6SDAP2.4 Use a variety of methods, such
as words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Act It Out
LUNCH Salvador is looking for his lunch money,
which he put in one of the pockets of his backpack
this morning. If the backpack has six pockets, what
is the probability that he will find the money in the
first pocket that he checks?
Explore You know that the backpack has six pockets
and that the lunch money is in one of the
pockets. You could act this out with a
spinner.
Plan
Spin a spinner numbered 1 to 6. If the
spinner lands on 1 he finds the lunch money
and if the spinner lands on 2, 3, 4, 5, or 6, he
does not find the lunch money. Repeat the
experiment 12 times.
Act It Out
Solve
Spin the spinner and make a table of the
results.
Act It Out
Check
Answer:
Repeat the experiment several times to see
if the results agree.
Thomas is randomly guessing at the correct answer
of a multiple-choice quiz question that has five
possible responses. What is the probability that he
selects the correct answer on his first try?
A.
B.
0%
D
A
B
0%
C
D
C
D.
A
0%
B
C.
A.
B.
0%
C.
D.
Five-Minute Check (over Lesson 9-6)
Main Idea and Vocabulary
California Standards
Example 1: Experimental Probability
Example 2: Experimental and Theoretical Probability
Example 3: Experimental and Theoretical Probability
Example 4: Real-World Example: Predict Future
Events
Example 5: Real-World Example: Predict Future
Events
• Find and compare experimental and theoretical
probabilities.
• theoretical probability
• experimental probability
Standard 6SDAP3.2 Use data to estimate the
probability of future events (e.g., batting averages or
number of accidents per mile driven).
Experimental Probability
A spinner is spun 50 times, and it lands on the
color blue 15 times. What is the experimental
probability of spinning blue?
Answer:
A marble is pulled from a bag of colored marbles 30
times, and 18 of the pulls result in a yellow marble.
What is the experimental probability of pulling a
yellow marble?
A.
B.
0%
D
A
B
0%
C
D
C
D.
A
0%
A.
B.
0%
C.
D.
B
C.
Experimental and Theoretical Probability
The graph below shows the results of an experiment
in which a number cube is rolled 30 times. Find the
experimental probability of rolling a 5.
Answer:
The graph shows the results of an experiment in
which a coin was tossed 150 times. Find the
experimental probability of tossing heads for this
experiment.
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Experimental and Theoretical Probability
Compare the experimental probability you found in
Example 2 to its theoretical probability.
Answer:
The graph shows the results of an
experiment in which a coin was
tossed 150 times. Compare the
experimental probability of tossing
heads to its theoretical probability.
A.
B.
.
1.
2.
3.
4.
.
0%
C.
D.
.
.
A
B
C
D
A
B
C
D
Predict Future Events
MOVIES In a survey, 50 people were asked to pick
which movie they would see this weekend. Twenty
chose Brad’s Story, 15 chose The Ink Well, 10
chose The Monkey House, and 5 chose Little
Rabbit. What is the experimental probability of
someone wanting to see The Monkey House?
There were 50 people surveyed and 10 chose The
Monkey House.
Answer:
SPORTS In a survey, 100 people were asked to pick
which sport they would watch on TV over the
weekend. Thirty-five chose football, 20 chose
basketball, 25 chose hockey, and 20 chose soccer.
What is the experimental probability of someone
wanting to watch football?
0%
D
0%
A
B
0%
C
D
C
D.
A.
B.
C.0%
D.
B
C.
B.
A
A.
Predict Future Events
Suppose 300 people are expected to attend a movie
theater this weekend to see one of the four movies.
How many can be expected to see The Monkey
House?
Write a proportion.
1 ● 300 = 5 ● x
300 = 5x
60 = x
Find the cross products.
Multiply.
Divide each side by 5.
Answer: About 60 people can be expected to see The
Monkey House.
In a survey, 100 people were asked to pick which
sport they would watch on TV over the weekend.
Thirty-five chose football, 20 chose basketball, 25
chose hockey, and 20 chose soccer. Suppose 1,500
people are expected to watch sports on TV this
weekend. How many can be expected to watch
football?
A. 300
B. 375
C. 525
0%
D
0%
C
A
0%
B
0%
D. 500
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 9-7)
Main Idea and Vocabulary
California Standards
Example 1: Independent Events
Key Concept: Probability of Independent Events
Example 2: Real-World Example
Key Concept: Probability of Dependent Events
Example 3: Dependent Events
Example 4: Disjoint Events
Key Concept: Probability of Disjoint Events
• Find the probability of independent and dependent
events.
• compound event
• independent events
• dependent events
• disjoint events
Standard 6SDAP3.4 Understand that the
probability of either of two disjoint events
occurring is the sum of the two individual
probabilities and that the probability of one event
following another, in independent trials, is the
product of the two probabilities.
Standard 6SDAP3.5 Understand the
difference between independent and dependent
events.
Independent Events
The spinner to the right is spun and a
number cube is tossed. Find the
probability of spinning a C and rolling
a number less than 5.
P
P
A coin is tossed and a number cube is rolled. Find
the probability of tossing heads and rolling an even
number.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
LUNCH For lunch, Jessica may choose a turkey
sandwich, a tuna sandwich, a salad, or a soup. For
a drink, she can choose juice, milk, or water. If she
chooses a lunch and a drink at random, what is the
probability that she chooses a sandwich and juice?
Answer: The probability that she chooses a sandwich
and juice is
CLOTHES Zachary has a blue, a red, a gray, and a
white sweatshirt. He also has blue, red, and gray
sweatpants. If Zachary randomly pulls a sweatshirt
and a pair of sweatpants from his drawer, what is
the probability that they will both be blue?
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Dependent Events
SOCKS There are 4 black, 6 white, and 2 blue
socks in a drawer. José randomly selects two
socks without replacing the first sock. What is the
probability that he selects two white socks?
Since the first card is not replaced, the first event affects
the second event. These are dependent events.
number of white socks
total number of socks
number of white socks
after one is removed
total number of socks
after one is removed
Dependent Events
1
2
Answer: So, the probability of selecting two white socks
is
or about 22.7%.
GAMES Janet has a card game that uses a deck of 48
cards–16 red, 16 blue, and 16 green. If she randomly
selects two cards without replacing the first, what is
the probability that both are green?
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Disjoint Events
MONTHS A month of the year is randomly selected.
What is the probability of the month ending in the
letter Y or the letter R?
These are disjoint events since it is impossible to have a
month ending in both the letter Y and the letter R.
There are 8 favorable outcomes:
January, February, May, July,
September, October, November,
or December.
There are 12 possible outcomes.
Answer: So, the probability of a month ending in the
letter Y or R is
.
MARBLES There are 12 yellow, 3 black, 5 red, and 8
blue marbles in a bag. Joseph randomly selects one
marble from the bag. What is the probability that the
marble selected will be black or red?
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Five-Minute Checks
Image Bank
Math Tools
Act It Out
Probability of Events
Lesson 9-1
(over Chapter 8)
Lesson 9-2
(over Lesson 9-1)
Lesson 9-3
(over Lesson 9-2)
Lesson 9-4
(over Lesson 9-3)
Lesson 9-5
(over Lesson 9-4)
Lesson 9-6
(over Lesson 9-5)
Lesson 9-7
(over Lesson 9-6)
Lesson 9-8
(over Lesson 9-7)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
(over Chapter 8)
Refer to the table shown in the
figure. Which choice shows a
frequency table for the set of data?
0%
A.
B.
0%
C.
D.
A
B
0%
C
D
0%
D
D.
C
C.
B
B.
A
A.
(over Chapter 8)
Refer to the table shown in the
figure. Which choice shows a
line plot for the set of data?
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Chapter 8)
Find the mean, median, and
mode for the set of data.
A. 90; 99.4; 50
0%
B. 99.4; 90; 100
1.
2.
3.
4.
C. 90; 99.4; 50 and 100
D. 99.4; 90; 50 and 100
A
B
A
B
C
D
C
D
(over Chapter 8)
Which measure best represents the data?
A. mean
B. median
C. mode
D. range
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 9-1)
A 12-sided number die shows the numbers 1 through
12, with one number showing each time the die is
rolled. Find the probability P(7). Write as a fraction in
simplest form.
A.
B.
C.
0%
D
0%
C
0%
B
D.
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-1)
A 12-sided number die shows the numbers 1 through
12, with one number showing each time the die is
rolled. Find the probability P(multiple of 4). Write as
a fraction in simplest form.
A.
0%
1.
2.
3.
4.
B.
C.
D.
A
B
C
D
A
B
C
D
(over Lesson 9-1)
A 12-sided number die shows the numbers 1 through
12, with one number showing each time the die is
rolled. Find the probability P(not a prime number).
Write as a fraction in simplest form.
A.
0%
1.
2.
3.
4.
B.
C.
D.
A
B
C
D
A
B
C
D
(over Lesson 9-1)
A box of cookies contains 5 chocolate chip cookies,
5 peanut butter, and 5 sugar. When choosing a
cookie at random, which answer does not show
the probability of getting a peanut butter cookie?
A.
B. 0.33...
C.
0%
D
0%
C
%
0%
B
D.
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-2)
For the situation given, make a tree diagram to show the
sample space. Then give the total number of outcomes. picking
a cat or dog and choosing the colors black, brown, or spotted
A.
B.
0%
D
A
B
0%
C
D
C
D.
A
0%
A.
B.
0%
C.
D.
B
C.
(over Lesson 9-2)
Using the spinner, what is the
probability of spinning two odd
numbers in two spins?
A.
B.
1.
2.
3.
4.
0%
C.
D.
A
B
C
D
A
B
C
D
(over Lesson 9-2)
How many styles of sneakers are possible if Jared
can choose from high-top or low-top, shoelaces or
Velcro, and the colors black, white, and red?
A. 3
B. 6
C. 12
0%
1.
2.
3.
4.
A
D. 24
A
B
C
D
B
C
D
(over Lesson 9-3)
Use the Fundamental Counting Principle to find the
total number of outcomes for the given situation.
choosing North, South, East, or West and one of the
50 states
A. 50
B. 100
C. 150
0%
D
0%
C
0%
B
D. 200
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-3)
Use the Fundamental Counting Principle to find the
total number of outcomes for the given situation.
picking a day of the week and a month of the year
A. 168
0%
B. 84
C. 72
1.
2.
3.
4.
A
B
C
D
A
D. 42
B
C
D
(over Lesson 9-3)
Use the Fundamental Counting Principle to find the
total number of outcomes for the given situation.
choosing vanilla, strawberry, chocolate, or mint chip
ice cream with fudge, butterscotch, strawberry, or
whipped topping, in a cone or a cup
0%
A. 10
B. 16
C. 32
1.
2.
3.
4.
A
D. 50
A
B
C
D
B
C
D
(over Lesson 9-3)
Use the Fundamental Counting Principle to find the
total number of outcomes for the given situation.
plain, barbeque, sour cream and onion, or salt and
vinegar potato chips, rippled or regular, in a small
or large bag
A. 16
B. 32
C. 36
0%
D
0%
C
0%
B
D. 64
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-3)
Margarita wants to wear a different outfit to school
each day using her new clothes. Margarita bought 5
pairs of pants, 9 shirts, and 4 pairs or shoes. How
many days of school does Margarita expect to have?
A. 60
0%
1.
2.
3.
4.
B. 90
C. 120
D. 180
A
B
C
D
A
B
C
D
(over Lesson 9-3)
Ryan has a business screen printing T-shirts. Ryan
offers 12 color options, 3 T-shirt styles, and printing
in 1, 2, 3, 4, or 5 colors. How many different styles of
shirt does Ryan’s business offer?
A. 36
0%
1.
2.
3.
4.
B. 64
C. 144
D. 180
A
B
C
D
A
B
C
D
(over Lesson 9-4)
How many permutations are possible of the letters
in the word answer?
A. 36
B. 720
C. 360
D. 120
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 9-4)
Julie, Dan, Janet, Kevin, and Michael all enter a
contest. Their names are pulled out of a hat one at
a time. What is the probability that Kevin’s name is
pulled first, then Dan’s?
A.
B.
C.
0%
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 9-4)
A child has the magnetic letters V, O, L, E. Find the
probability that the child randomly arranges the
letters in the order of love.
A.
B.
C.
0%
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 9-4)
Carlos, Sierra, David, and Nicole go to the movies and will
sit in a row of four seats. If each friend is equally-likely to
sit in any seat, what is the probability that David will sit in
the first seat and Nicole will sit in the second seat?
A.
B.
C.
0%
D
0%
C
A
D.
0%
B
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-4)
In how many ways can a football coach arrange the
first five players in a lineup of eleven players?
A. 120
0%
B. 55,440
C. 332,640
D. 39,916,800
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 9-5)
State whether the problem represents a
permutation or combination and then solve it. How
many ways can you arrange the 7 natural notes in a
musical scale for a three-note arrangement without
repeating a note?
A. permutation; 210
B. combination; 210
C. permutation; 840
0%
D
0%
C
0%
B
D. combination; 840
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-5)
State whether the problem represents a permutation
or combination and then solve it. There are 10
people in a club. In how many ways can a committee
of 5 be chosen from the 10 people?
A. permutation; 30,240
B. combination; 30,240
C. permutation; 252
D. combination; 252
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 9-5)
You are a judge in a battle of the bands. There are 6
bands. You must choose 1st, 2nd, and 3rd place.
How many different results can you choose?
A. 20
0%
1.
2.
3.
4.
B. 36
C. 120
A
D. 360
B
A
B
C
D
C
D
(over Lesson 9-5)
What is the difference between a permutation and a
combination?
A. In permutations and
combinations, order is
important.
B. In a combination, order is
important.
0%
D
A
B
0%
C
D
C
A
D. In a combination, order is not
important.
0%
B
C. In a permutation, order is not
important.
A.
B.
0%
C.
D.
(over Lesson 9-5)
How many ways can a coach select 4 members of a
12-person team to go to the State Competition?
A. 24
0%
B. 495
C. 11,880
D. 479,001,600
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 9-6)
Four friends all shake hands with one another. How
many handshakes take place? Solve by acting it out.
A. 6
B. 24
C. 12
D. 8
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 9-6)
Liz needs to clean her room, walk the dog, and do
her homework. How many ways can she do these
three things? Solve by acting it out.
A. 3
0%
B. 9
C. 6
1.
2.
3.
4.
A
B
C
D
A
D. 5
B
C
D
(over Lesson 9-6)
Five friends ran a race. How many possible ways
could the friends have finished the race? Solve by
acting it out.
A. 25
0%
1.
2.
3.
4.
B. 20
C. 120
A
D. 125
B
A
B
C
D
C
D
(over Lesson 9-6)
Diego bought a pair of $58 jeans at a sale price of
$47. What was the approximate percent of decrease
from the original price to the sale price?
A. 20%
B. 25.2%
C. 19%
0%
D
0%
C
0%
B
D. 23.4%
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-6)
Three students are to be chosen from auditions of
9 students to be leads in the school play. In how
many ways can these three students be chosen?
A. 84
0%
B. 54
C. 81
1.
2.
3.
4.
A
B
C
D
A
D. 27
B
C
D
(over Lesson 9-7)
A number cube is tossed 24 times and lands on 1
three times and on 2 four times. Find the
experimental probability of landing on 1.
A.
B.
C.
0%
D
0%
C
0%
B
D.
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-7)
A number cube is tossed 24 times and lands on 1
three times and on 2 four times. Find the theoretical
probability of not landing on 1.
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 9-7)
A number cube is tossed 24 times and lands on 1
three times and on 2 four times. Find the theoretical
probability of landing on 2.
A.
0%
1.
2.
3.
4.
B.
C.
A
D.
B
A
B
C
D
C
D
(over Lesson 9-7)
A number cube is tossed 24 times and lands on 1
three times and on 2 four times. Find the
experimental probability of not landing on 2.
A.
B.
C.
0%
D
0%
C
0%
B
D.
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 9-7)
State the difference between theoretical and experimental
probabilities.
A.
B.
C.
D.
An experimental probability is based on
information gained by an experiment or game,
while a theoretical probability is made without
referring to any data.
An experimental probability is determined
using mathmatical methods, while a theoretical
probability is determined by performing
experiments.
The event which is possible for experiment is
said to have experimental probability and in
which experiment is not possible, it is said to
have theoretical probability.
An experimental probability is made without
referring to any data while theoretical
probability is based on information related to
the data.
1.
2.
3.
4.
A
B
C
D
A
0%
B
C
D
(over Lesson 9-7)
In one afternoon, 24 restaurant customers order
steak, 18 order sandwiches, and 20 order salads.
Based on this, what is the probability that the next
patron will order a salad?
0%
A.
B.
C.
1.
2.
3.
4.
A
D.
A
B
C
D
B
C
D
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