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Lesson 16-1 Probability and OutcomesLesson 16-2 Probability and FractionsLesson 16-3 Problem-Solving Strategy:
Make an Organized ListLesson 16-4 Find ProbabilityLesson 16-5 Problem-Solving
Investigation: Choose a StrategyLesson 16-6 Tree Diagrams
16Probability
Five-Minute Check (over Chapter 15)Main Idea and VocabularyCalifornia StandardsExample 1Example 2
16-1 Probability and Outcomes
16-1 Probability and Outcomes
• I will describe probability.
• outcome• probability
16-1 Probability and Outcomes
Standard 4SDAP1.2 Express outcomes of
experimental probability situations verbally and
numerically (e.g., 3 out of 4; ).
16-1 Probability and Outcomes
Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
There are 10 marbles and 8 are green.
Kimmela has 8 green and 2 white marbles. Describe how likely it is that Kimmela will choose a green marble.
16-1 Probability and Outcomes
Answer: So, it is likely that Kimmela will choose a green marble.
16-1 Probability and Outcomes
Lexie has a bag with 7 blue marbles and 7 red marbles. Describle how likely it is that Lexie will choose a red marble.
A. certain
B. likely
C. equally likely
D. not likely
Jeremiah has 15 coins in his pocket. 10 are dimes, 5 are nickels. If he drops a coin on the ground, describe the probability that the coin is a penny.
There are 15 coins in Jeremiah’s pocket. Of those coins, none of them are pennies.
Answer: Since there are no pennies, it is impossible that Jeremiah dropped a penny.
16-1 Probability and Outcomes
16-1 Probability and Outcomes
Luna has 12 coins in her pocket. All of them are dimes. If she drops a coin on the ground, describe the probability that the coin is a dime.
A. impossible
B. likely
C. unlikely
D. certain
Five-Minute Check (over Lesson 16-1)Main Idea and VocabularyCalifornia StandardsKey Concepts: Probability as a FractionExample 1Example 2
16-2 Probability and Fractions
16-2 Probability and Fractions
• I will describe probability in words and in numbers.
• favorable outcome
16-2 Probability and Fractions
Standard 4SDAP2.2 Express outcomes of
experimental probability situations verbally and
numerically (e.g., 3 out of 4; ).
16-2 Probability and Fractions
Use words and a fraction to describe the probability of rolling a 5 on a number cube.
One out of six numbers on a number cube is a 5.
16-2 Probability and Fractions
Probability = favorable outcomestotal possible outcomes
= roll a 5roll any number
= 16
16-2 Probability and Fractions
Answer: So, the probability of rolling a 5 on a
number cube is 1 out of 6 or , which
is unlikely.
16
16-2 Probability and Fractions
Use words and a fraction to describe the probability of tossing a coin and getting heads.
A. certain; 22
B. equally likely; 12
C. equally likely; 14
D. impossible; 02
In a bucket of tennis balls, there are 10 yellow, 6 green, and 4 purple balls. Ms. Gorman reaches in without looking and chooses one. Use words and a fraction to describe the probability of choosing a purple tennis ball.
Four out of twenty tennis balls are purple.
16-2 Probability and Fractions
16-2 Probability and Fractions
Probability = favorable outcomestotal possible outcomes
= purple tennis ballsevery color of tennis balls
= 420
Answer: So, the probability of choosing a purple
tennis ball is , or 4 out of 20.420
16-2 Probability and Fractions
Tammy has a jar in her room with 5 nickels, 10 pennies, and 2 dimes. She reaches into her jar without looking and chooses one. Use words and a fraction to describe the probability of choosing a penny.
A. likely; 1017
B. likely; 517
C. unlikely; 217
D. unlikely; 1017
Five-Minute Check (over Lesson 16-2)Main IdeaCalifornia StandardsExample 1: Problem-Solving Strategy
16-3 Problem-Solving Strategy: Make an Organized List
16-3 Problem-Solving Strategy: Make an Organized List
• I will make an organized list to solve problems.
16-3 Problem-Solving Strategy: Make an Organized List
Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
16-3 Problem-Solving Strategy: Make an Organized List
Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g. tables, grids, tree diagrams).
The Burke family is going camping for the weekend. There are four children in the Burke family, Zane, Nora, Olga, and Peter. They will sleep in two tents, with two children in each tent. How many different combinations are possible?
16-3 Problem-Solving Strategy: Make an Organized List
Understand
What facts do you know?• There are 4 children.• Two children will sleep in each tent.
What do you need to find?• Find how many combinations are possible.
16-3 Problem-Solving Strategy: Make an Organized List
Plan
You can make a list of all the possible combinations. Then count the total number of different combinations.
16-3 Problem-Solving Strategy: Make an Organized List
Solve
First, write the name of one of the children. Then, write the name of another child by the first child’s name. Continue to do this with each child. Do not repeat pairs.
16-3 Problem-Solving Strategy: Make an Organized List
Solve
Nora–Olga
Nora–Peter
Nora–Zane
Answer: There are 6 different combinations who can be in each tent.
16-3 Problem-Solving Strategy: Make an Organized List
Olga–Peter
Olga–Zane
Peter–Zane
Check
Look back at the problem. There are 4 children. They can each pair up with three other children. Each child’s name does appear 3 times on the list. So, the answer is correct.
16-3 Problem-Solving Strategy: Make an Organized List
Five-Minute Check (over Lesson 16-3)Main Idea and VocabularyCalifornia StandardsExample 1Example 2
16-4 Find Probability
16-4 Find Probability
• I will find the probability of outcomes using a grid.
• grid
16-4 Find Probability
Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
16-4 Find Probability
Standard 4SDAP2.2 Express outcomes of
experimental probability situations verbally and
numerically (e.g., 3 out of 4; ).
Sari chose two flowers from the bucket of half pink, half red flowers without looking. Use the grid to find the probability she chose two pink flowers.
16-4 Find Probability
There are four possible color combinations. Red and red, red and pink, pink and red, and pink and pink.
One of the outcomes is pink and pink.
16-4 Find Probability
Probability = favorable outcomestotal possible outcomes
= 14
Answer: So, the probability is 1 out of 4, or .14
16-4 Find Probability
Use the grid to find the probability of tossing two coins and getting tails on both.
A. 14
16-4 Find Probability
Use the grid to find the probability of tossing two coins and getting tails on both.
B. 24
C. 34
D. 44
Create a grid to show all possible outcomes of flipping a coin and rolling a number cube. Then use the grid to find the probability of getting heads and a number greater than 2.
16-4 Find Probability
Step 1 Write the possible outcomes for a coin on the side of the grid and the outcomes for a number cube on the top of the grid.
Step 2 Write the possible outcomes for tossing a coin and rolling a die in the squares where each row and column intersect.
16-4 Find Probability
16-4 Find Probability
Answer: There are 12 possible outcomes. Four of the
outcomes are getting a heads and rolling a
number greater than 2. So, the probability is
4 out of 12 or .4
12
16-4 Find Probability
Use the grid to find the probability of getting tails and an even number.
A. 9
12
B. 6
12
C. 3
12
D. 1
12
Five-Minute Check (over Lesson 16-4)Main IdeaCalifornia StandardsExample 1: Problem-Solving Investigation
16-5 Problem-Solving Investigation: Choose a Strategy
16-5 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
16-5 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, and prioritizing information, and observing patterns.
16-5 Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve problems involving addition, subtraction, of whole numbers and understand the relationships among the operations.
CARMEN: My family ate dinner at a restaurant. We ordered salads for $6 each, steaks for $15 each, and chicken sandwiches for $8 each. The total cost was $43.
YOUR MISSION: Find how many of each item was ordered.
16-5 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?• You know the cost of each item.• You know the total cost of the meal.
What do you need to find?
• You need to find how many of each item was ordered.
16-5 Problem-Solving Investigation: Choose a Strategy
Plan
Use logical reasoning to find how many of each item was ordered.
16-5 Problem-Solving Investigation: Choose a Strategy
Solve
At least one of each item was ordered. Add the costs.
16-5 Problem-Solving Investigation: Choose a Strategy
$15 + $6 + $8 = $21 + $8
= $29
So, the cost of the other items ordered must be $43 – $29, or $14.
Solve
Since $8 + $6 is the only combination of costs that equal $14, you know that another salad and chicken sandwich were ordered.
16-5 Problem-Solving Investigation: Choose a Strategy
Answer: So, Carmen’s family ordered 1 steak, 2 salads, and 2 chicken sandwiches.
Check
You can check your answer with addition.
16-5 Problem-Solving Investigation: Choose a Strategy
$6 + $6 + $8 + $8 + $15 = $43
So, the answer is correct.
Five-Minute Check (over Lesson 16-5)Main Idea and VocabularyCalifornia StandardsExample 1Example 2
16-6 Tree Diagrams
16-6 Tree Diagrams
• I will use a tree diagram to show outcomes.
• tree diagram
16-6 Tree Diagrams
Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
16-6 Tree Diagrams
Standard 4SDAP2.2 Express outcomes of
experimental probability situations verbally and
numerically (e.g., 3 out of 4; ).
How many outcomes are possible when both spinners are spun?
16-6 Tree Diagrams
Use a tree diagram to find the possible outcomes.
List each color on each of the spinners. Then pair each color choice from one spinner to each color choice on the other spinner.
16-6 Tree Diagrams
Spinner 1
16-6 Tree Diagrams
Red (R)Red (R2)Blue (B2)Purple (P)
R, R2R, B2R, P
Orange (O)Red (R2)Blue (B2)Purple (P)
O, R2O, B2O, P
Spinner 2 Outcome
16-6 Tree Diagrams
Yellow (Y)Red (R2)Blue (B2)Purple (P)
Y, R2Y, B2Y, P
Light blue (L)Red (R2)Blue (B2)Purple (P)
L, R2L, B2L, P
Blue (B)Red (R2)Blue (B2)Purple (P)
B, R2B, B2B, P
16-6 Tree Diagrams
Michelle has a coin and bag of marbles with 1 yellow, 1 blue, 1 red, 1 green, and 1 purple. How many outcomes are possible when the coin is tossed and one marble is drawn?
A. 6
B. 8
C. 10
D. 12
Kasim is flipping three coins. Make a tree diagram and use it to find the probability of flipping at least two heads.
16-6 Tree Diagrams
16-6 Tree Diagrams
Coin 1 Coin 2 Coin 3
Heads
HeadsHeads
Tails
Tails
Heads
Tails
Tails
HeadsHeads
Tails
Tails
Heads
Tails
16-6 Tree Diagrams
There are eight possible outcomes. Four of these outcomes has at least two heads: HHH, HHT, HTH, and THH.
=at least 2 heads
total possible outcomes
Answer: So, the probability is 4 out of 8, or .48
16-6 Tree Diagrams
Noel is flipping two coins and spinning the spinner below. Find the probability of getting heads on one coin, tails on the other, and landing on red.
B. 26
C. 46
A. 412
D. 2
12
16Probability
Five-Minute Checks
16Probability
Lesson 16-1 (over Chapter 15)
Lesson 16-2 (over Lesson 16-1)
Lesson 16-3 (over Lesson 16-2)
Lesson 16-4 (over Lesson 16-3)
Lesson 16-5 (over Lesson 16-4)
Lesson 16-6 (over Lesson 16-5)
16Probability
(over Chapter 15)
Subtract.
A. 0.1
B. 1.9
C. 1.1
D. 11
1.5 – 0.4
16Probability
(over Chapter 15)
A. 8.46
B. 5.04
C. 7.46
D. 6.04
Subtract.
6.75 – 1.71
16Probability
(over Chapter 15)
A. $10.19
B. $11.21
C. $11.11
D. $11.19
Subtract.
$22.38 – $11.19
16Probability
(over Chapter 15)
A. 3.7
B. 4.6
C. 3.6
D. 4.4
Subtract.
9.1 – 5.5
16Probability
(over Lesson 16-1)
Describe the probability of spinning a green.
A. impossible
B. certain
C. likely
D. unlikely
16Probability
(over Lesson 16-1)
Describe the probability of spinning a yellow.
A. impossible
B. certain
C. likely
D. unlikely
16Probability
(over Lesson 16-1)
Describe the probability of spinning a white.
A. impossible
B. certain
C. likely
D. unlikely
16Probability
(over Lesson 16-1)
Describe the probability of spinning a green, blue or yellow.
A. impossible
B. certain
C. likely
D. unlikely
16Probability
(over Lesson 16-2)
Use words or a fraction to describe the probability of spinning a green.
B. 4 out of 12
D. 4 out of 16
A. 415
C. 164
16Probability
Use words or a fraction to describe the probability of spinning a yellow.
(over Lesson 16-2)
D. 16 out of 10
A. 10 out of 6
B. 110
C. 1016
16Probability
Use words or a fraction to describe the probability of spinning a red.
(over Lesson 16-2)
B. 2 out of 14
D. 2 out of 15
A. 216
C. 162
16Probability
Use words or a fraction to describe the probability of spinning a blue.
(over Lesson 16-2)
B. unable to describe probability
D. 16 out of 0
A. 116
C. 0
16Probability
(over Lesson 16-3)
Solve. Use the Make an Organized List strategy. Lunch choices include ham, turkey, or cheese sandwiches and one of the following: carrots, an apple, chips, or a cookie. How many different lunch combinations are possible?
A. 7
B. 9
C. 12
D. 18
16Probability
(over Lesson 16-4)
Use the grid to find the probability of spinning vanilla with berries.
16Probability
(over Lesson 16-4)
Use the grid to find the probability of spinning vanilla with berries.
A. The probability of spinning vanilla with
berries is 2 out of 12.
B. The probability of spinning vanilla
with berries is .412
16Probability
(over Lesson 16-4)
Use the grid to find the probability of spinning vanilla with berries.
C. The probability of spinning vanilla
with berries is 0.
D. The probability of spinning vanilla
with berries is .112
16Probability
(over Lesson 16-4)
Use the grid to find the probability of spinning vanilla with berries.
D. The probability of spinning vanilla
with berries is .112
16Probability
(over Lesson 16-5)
Solve. Gabriela has four different plants but only has room in the garden to plant three of them. She needs to decide which three to plant. How many ways can she choose 3 of the 4 plants?
A. 3
B. 4
D. 12
C. 34
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