Transcript 6th_MA_SDP_3.1_REPRESENT_OUTCOMES_DW

Name___________________
Learning Objective
Today, we will represent1 outcomes for compound events.
1
show
CFU
What are we doing to do today?
What does represent mean? Represent means_______________.
Activate (or provide) Prior Knowledge
1. If I have 10 Snickers and 2 Butterfingers in a bag, which one will I most likely grab?
I will most likely grab a Snickers.
2. If you have 9 pairs of black socks and 4 pairs of blue socks, what color pair will you
most likely grab?
You will most likely grab a pair of black socks.
CFU
These are both single events, they ask about one thing happening. You were all able to identify how likely it is that some event will occur,
which is called probability. Today, we will represent outcomes and calculate probability for more than one event, called compound events.
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6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Concept Development
A compound event consists2 of two or more events.
2
is made up of
Probability is the likelihood that an event will happen.
Probability = number of desired3 outcomes
total number of outcomes
3
wanted
Outcomes are possible results. They are what could happen in a given compound event.
• Tables and tree diagrams can be used to show how many outcomes are likely.
Example: If two coins are tossed, what is the probability of both coins landing heads up?
tree diagram
table
Coin 1 Coin 2
Coin 1:
Tails
Heads
1. Heads Heads
2. Heads Tails
3. Tails
Heads
4. Tails
Tails
Coin 2:
Heads
Tails
Heads
Tails
1. Heads/Heads 2. Heads/Tails 3. Tails/Heads 4. Tails/Tails
The probability for the compound event of both coins landing heads up is 1 .
4
CFU
Which is an example of a compound event? How do you know?
1. Rolling a die and spinning a spinner
2. Rolling a die
In your own words, explain what outcomes are. Outcomes are __________________________________.
In your own words, explain what probability is. Probability is _________________.
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6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify 4 the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine5 the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
4
find
5
figure out
1. Mike is ordering ice cream at a local ice cream store. If he can select one flavor and one topping, what is the
probability that he will choose chocolate ice cream with peanuts. Create a tree diagram to show all the possible
choices of ice cream combinations.
Flavor
Topping
Chocolate
Sprinkles
Vanilla
Butterscotch
Peanuts
C
V
Outcomes for first event:
S
B
P
S
B
P
Outcomes for second event:
All outcomes for the compound event: ___________________________________________________________________________
CS, CB, CP, VS, VB, VP
1
The probability for the compound event of choosing chocolate and peanuts is __________.
6
CFU
(#1) How did I/you identify the desired outcome?
(#3) How did I/you list all the outcomes for the compound event?
(#4)How did I/you identify the desired outcome for the compound event?
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
Probability = number of desired outcomes
total number of outcomes
A compound event consists of two or more events.
Outcomes are possible results
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
2. At a deli, customers can choose one meat and one cheese for a sandwich. What is the probability that a
sandwich will have turkey and Swiss cheese? Create a tree diagram to show all possible sandwich combinations.
Meat
Cheese
Ham
Swiss
Beef
Cheddar
Turkey
Provolone
H
B
T
Outcomes for first event:
S
C
P
S
C
P
S
C
P
Outcomes for second event:
All outcomes for the compound event: ___________________________________________________________________________
HS, HC, HP, BS, BC, BP, TS, TC, TP
1
The probability for the compound event of a sandwich with turkey and Swiss cheese is _______.
9
CFU
(#1) How did I/you identify the desired outcome?
(#3) How did I/you list all the outcomes for the compound event?
(#4)How did I/you identify the desired outcome for the compound event?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
Probability = number of desired outcomes
total number of outcomes
A compound event consists of two or more events.
Outcomes are possible results.
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
3. Sam is ordering ice cream at a local ice cream store. If he can select one flavor and one topping, what is the
probability that he will choose vanilla or chocolate ice cream and not butterscotch topping? Create a table to
show all the possible choices of ice cream combinations.
Flavor
Topping
Chocolate
Sprinkles
Vanilla
Butterscotch
Peanuts
Outcomes for first event
Outcomes for second event
C
C
C
V
V
V
S
B
P
S
B
P
CS, CB, CP, VS, VB, VP
All outcomes for the compound event: ____________________________________________________________
4
2
or
The probability for the compound event of choosing vanilla or chocolate and not butterscotch is _______.
6
3
CFU (#1) How did I/you identify the desired outcome?
(#3) How did I/you list all the outcomes for the compound event?
(#4)How did I/you identify the desired outcome for the compound event?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
A compound event consists of two or more events.
Outcomes are possible results.
Represent outcomes for compound events.
Probability = number of desired outcomes
total number of outcomes
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
4. At a deli, customers can choose one meat and one cheese for a sandwich. What is the probability that a
sandwich will have beef and not cheddar cheese? Create a table to show all possible sandwich combinations.
Outcomes for first event
Outcomes for second event
S
C
Meat
Cheese
Ham
Swiss
H
H
Beef
Cheddar
H
P
Turkey
Provolone
B
S
C
B
B
T
T
T
P
S
C
P
HS, HC, HP, BS, BC, BP, TS, TC, TP
All outcomes for the compound event: ___________________________________________________________________________
2
The probability for the compound event of a sandwich having beef and not cheddar is ________.
9
CFU (#1) How did I/you identify the desired outcome?
(#3) How did I/you list all the outcomes for the compound event?
(#4)How did I/you identify the desired outcome for the compound event?
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Relevance
A compound event consists of two or more events.
Outcomes are possible results.
1. Representing outcomes for compound events
will help you in other classes, like Biology,
when we determine inherited traits.
2. Representing outcomes for compound
events will help you do well on tests.
Pea plants can either be tall or short. The
peas inherit the traits from their parent
plants. To have a short plant, they have to
get the short trait from both parents.
T
t
T
TT
Tt
t
Tt
tt
There is one of the four offspring above that
has both short traits. The probability of
having a short pea plant is 1 .
4
CFU
Does anyone else have another reason why it is relevant to represent outcomes for compound events? (pair-share) Why is it relevant to
represent outcomes for compound events? You may give me one of my reasons or your own reason. Which reason is more relevant to
you? Why?
DataWORKS Educational Research
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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©2012 All rights reserved.
Comments? [email protected]
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.
Lesson to be used by EDI-trained teachers only.
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Skill Closure
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
1. An automobile dealer has cars available with a combination of colors and engines. What is the probability that a person will buy a
car that has a 6-cylinder engine and is red? Create a tree diagram to show all the possible choices of cars.
4
Outcomes for first event:
Outcomes for second event:
R
B
6
S
W
R
B
S
Engine
Color
4-cylinder
Red
6-cylinder
Black
W
Silver
White
4B, 4S, 4W, 6R, 6B, 6S, 6W
All outcomes for the compound event: 4R,
_________________________________________________________________________
1
The probability for the compound event of buying a car that has a 6-cylinder engine and is red is ________.
8
Constructed Response Closure
Using a tree diagram to represent outcomes, Olivia identified 5 different choices in sandwiches. Is she correct or incorrect?
Explain your answer.
Ham
Swiss
Turkey
Cheddar
Swiss
Cheddar
What did you learn today about representing outcomes for compound events? (pair-share)
Day 1______________________________________________________________________________
Day 2______________________________________________________________________________
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Independent Practice
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
1. At a restaurant, customers can choose one sandwich and one drink for a lunch combo. What is the probability
that a person will choose a bologna sandwich and a soda? Create a tree diagram to show all possible sandwich
combinations.
Sandwich
Drink
Turkey
Root beer
Bologna
Water
Egg
Lemonade
Cola
Outcomes for first event:
Outcomes for second event: R
T
W
B
L
C
R
W
E
L
C
R
W
L
C
All outcomes for the compound event: ___________________________________________________________
TR, TW, TL, TC, BR, BW, BL, BC, ER, EW, EL, EC
2
1
or
The probability for the compound event of choosing a bologna sandwich and a soda is ________.
12
6
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Independent Practice (continued)
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
2. All raffle tickets for an upcoming drawing must have one number from column A and one number from column
B. What is the probability that a person will choose a ticket with a number less than 5 from column A and greater
than 5 from column B? Create a table to show all possible number combinations.
A
B
2
1
3
6
8
Outcomes for first event
Outcomes for second event
2
2
1
6
3
1
3
8
6
1
8
6
All outcomes for the compound event: ____________________________________________________________
2-1, 2-6, 3-1, 3-6, 8-1, 8-6
The probability for the compound event of choosing a ticket with a number less than 5 from column A and greater
2
1
or
6
3
than 5 from column B is ________.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 1
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
1. The local city college requires every student to take a foreign language and a science course. What is the
probability that a person will take German and Astronomy? Create a tree diagram to show all possible course
combinations.
Foreign Language
Science
German
Astronomy
Spanish
Biology
Japanese
French
Outcomes for first event:
Outcomes for second event:
S
G
A
B
A
F
J
B
A
B
A
B
All outcomes for the compound event: ___________________________________________________________
GA, GB, SA, SB, JA, JB, FA, FB
1
The probability for the compound event of taking German and Astronomy is __________.
8
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1 (continued)
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
2. At a pizza restaurant, customers can choose
one topping from each column to make a
combination pizza. What is the probability that a
person will choose a pizza with meat from
column 1 and meat from column 2? Create a
table to show all possible pizza combinations.
Outcomes for first event
Outcomes for second event
B
C
O
B
C
O
B
C
O
Column 1
Column 2
Pepperoni
Bacon
P
P
P
T
T
T
Tomato
Chicken
H
Ham
Olives
H
H
Sausage
S
All outcomes for the compound event:
_______________________________________
PB,
PC, PO, TB, TC, TO, HB, HC, HO, SB,
_______________________________________
SC,
SO
The probability for the compound event of
choosing a pizza with only meat is 6 or 1
12
2
______.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
S
S
B
C
O
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 2
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
1. At a pizza restaurant, customers can choose one topping from each column to make a combination pizza. What
is the probability that a person will choose a pizza with no tomatoes and no olives? Create a tree diagram to show
all possible pizza combinations.
Column 1
Column 2
Pepperoni
Bacon
Tomato
Chicken
Ham
Olives
Sausage
Outcomes for first event:
Outcomes for second event:
P
B
C
T
O
B
C
S
H
O
B
C
O
B
C
O
All outcomes for the compound event: ___________________________________________________________
PB, PC, PO, TB, TC, TO, HB, HC, HO, SB, SC, SO
6
1
or
12
2
The probability for the compound event of choosing a pizza with no tomatoes and no olives is __________.
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2 (continued)
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
2. At a restaurant, customers can choose one
sandwich and one drink for a lunch combo. What
is the probability that a person will choose an egg
sandwich and not a soda? Create a table to show
all possible sandwich combinations.
Sandwich
Drink
Turkey
Root beer
Bologna
Water
Egg
Lemonade
Cola
All outcomes for the compound event:
TR,
TW, TL, TC, BR, BW, BL, BC, ER, EW, EL,
________________________________________
EC
________________________________________
The probability for the compound event of
choosing an egg sandwich and not a soda is
2
1
or
12
6
______.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
Outcomes for first event
Outcomes for second event
T
T
T
T
B
B
B
B
R
W
L
C
R
W
L
C
E
E
E
E
R
W
L
C
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 3
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
1. All raffle tickets for an upcoming drawing must have one number from column A and one number from column
B. What is the probability that a person will choose a ticket with an even number from column A and an odd
number from column B? Create a tree diagram to show all possible number combinations.
B
2
1
3
6
8
Outcomes for first event:
Outcomes for second event:
A
2
1
8
3
6
1
6
1
6
All outcomes for the compound event: 2-1,
___________________________________________________________
2-6, 3-1, 3-6, 8-1, 8-6
The probability for the compound event of choosing a ticket with an even number from column A and an odd
number from column B is 2
1
or
__________.
6
3
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3 (continued)
A compound event consists of two or more events.
Outcomes are possible results.
Probability = number of desired outcomes
total number of outcomes
Represent outcomes for compound events.
Step #1: Read the question and identify the desired outcome. (underline)
Step #2: Use a tree diagram or a table to determine the outcomes.
Step #3: List all the outcomes for the compound event.
Step #4: Identify all the desired outcomes meeting the requirements of the question.(circle)
Step #5: Set up a fraction to determine the probability of the event.
2. The local city college requires every student to
take a foreign language and a science course.
What is the probability that a person will not take
Japanese and will take either Biology or
Astronomy? Create a table to show all possible
course combinations.
Foreign Language
Science
German
Astronomy
Spanish
Biology
Japanese
Outcomes for first event
Outcomes for second event
G
G
S
S
J
A
B
A
B
A
B
J
F
F
A
B
French
All outcomes for the compound event: ____________________________________________________________
GA, GB, SA, SB, JA, JB, FA, FB
6 3
or
The probability for the compound event of not taking Japanese and taking either Astronomy or Biology is ________.
8 4
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Statistics, Data Analysis, and Probability 3.1 (1Q)
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.
Lesson to be used by EDI-trained teachers only.