Geometry (& GT)
Unit 5: Applications of Probability
Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.
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What will my child learn?
Students will:
Part I: Probability of Compound Events
Understand independence and conditional probability and use them to interpret data.
S.CP.A.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”).
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
Understand independence and conditional probability and use them to interpret data.
S.CP.A.2
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.A.4
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results (SAT® Content - PSDA.07).
Understand independence and conditional probability and use them to interpret data.
S.CP.A.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B.6
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.8 (+)
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. (Geometry GT)
S.CP.B.9 (+)
Use permutations and combinations to compute probabilities of compound events and solve problems. (Geometry GT)
Use probability to evaluate outcomes of decisions. (Geometry GT)
S.MD.B.6 (+)
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (Geometry GT)
S.MD.B.7 (+)
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulled a hockey goalie at the end of a game). (Geometry GT)
Students will:
Part I: Probability of Compound Events
Understand independence and conditional probability and use them to interpret data.
S.CP.A.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”).
- Background Info.
- Check for Understanding: Basic Set Notation | Describing Subsets of Sample Spaces
- Review/Rewind: Intersection and Union of Sets
- Enrichment Tasks: The Titanic 1
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
- Background Info.
- Check for Understanding: Adding Probabilities
- Review/Rewind: Addition Rule for Probability
- Enrichment Tasks: Venn Diagrams and the Addition Rule
Understand independence and conditional probability and use them to interpret data.
S.CP.A.2
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
- Background Info.
- Check for Understanding: Identifying Dependent and Independent Events
- Review/Rewind: Analyzing Event Probability for Independence
- Enrichment Tasks: Cards and Independence | The Titanic 2
S.CP.A.4
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results (SAT® Content - PSDA.07).
- Check for Understanding: Trends in Categorical Data
- Review/Rewind: Filling Out Frequency Table for Independent Events
- Enrichment Tasks: The Titanic 3 | How do you Get to School?
Understand independence and conditional probability and use them to interpret data.
S.CP.A.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
- Background Info.
- Check for Understanding: Identifying Dependent and Independent Events
- Review/Rewind: Independent and Dependent Probability
- Enrichment Tasks: FInding Probabilities of Compound Events | Lucky Envelopes
S.CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
- Background Info.
- Check for Understanding: Trends in Categorical Data
- Review/Rewind: Analyzing Trends in Categorical Data
- Enrichment Tasks: Breakfast Before School | But Mango is My Favorite....
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B.6
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
- Background Info.
- Check for Understanding: Dependent Probability | Trends in Categorical Data
- Review/Rewind: Dependent Probability Introduction
- Enrichment Tasks: How Do You Get to School? | The Titanic 3
S.CP.B.8 (+)
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. (Geometry GT)
- Check for Understanding: Multiplying Dependent Probabilities
- Review/Rewind: Calculating Conditional Probability
- Enrichment Tasks:
S.CP.B.9 (+)
Use permutations and combinations to compute probabilities of compound events and solve problems. (Geometry GT)
- Check for Understanding: Permutations and Combinations | Probability with Permutations and Combinations
- Review/Rewind: Probability Using Combinations
- Enrichment Tasks: Alex, Mel, and Chelsea Play a Game | Random Walk IV
Use probability to evaluate outcomes of decisions. (Geometry GT)
S.MD.B.6 (+)
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (Geometry GT)
- Check for Understanding: Using Probability to make Fair Decisions
- Review/Rewind: Picking Fairly
- Enrichment Tasks
S.MD.B.7 (+)
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulled a hockey goalie at the end of a game). (Geometry GT)
- Check for Understanding: Making Decisions with Expected Values | Using Probability to Make Fair Decisions
- Review/Rewind: Term Life Insurance and Death Probability
- Enrichment Tasks: Fred's Fun Factory
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What are some signs of student mastery?
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Tools & Technology
Shodor Interactive - provides an interactive platform for exploring mathematical concepts View how the following tools are used to help students:
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More 4 U
Looking for clarification on some of the vocabulary used in the Geometry course? A slight variation in units, click here to download the MD State Department of Education's (MSDE's) geometry glossary. |
