# Modeling Conditional Probabilities 1: Lucky Dip

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## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution-NonCommercial-NoDerivs 3.0
- Media Format:
- Downloadable docs, Text/HTML

## Standards

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

Standard: 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”).*

Degree of Alignment: 3 Superior (1 user)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Use probability to evaluate outcomes of decisions

Standard: (+) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Standard: (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Standard: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Use probability to evaluate outcomes of decisions

Standard: (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityStandard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Use probability to evaluate outcomes of decisions

Standard: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Use probability to evaluate outcomes of decisions

Standard: (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Use probability to evaluate outcomes of decisions

Standard: (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Calculate expected values and use them to solve problems

Standard: (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Calculate expected values and use them to solve problems

Standard: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Calculate expected values and use them to solve problems

Standard: (+) Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Using Probability to Make DecisionsCluster: Calculate expected values and use them to solve problems

Standard: (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Use probability to evaluate outcomes of decisions

Indicator: (+) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Use probability to evaluate outcomes of decisions

Indicator: (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Use probability to evaluate outcomes of decisions

Indicator: (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Use probability to evaluate outcomes of decisions

Indicator: (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Use probability to evaluate outcomes of decisions

Indicator: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Indicator: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Indicator: (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Calculate expected values and use them to solve problems

Indicator: (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Calculate expected values and use them to solve problems

Indicator: (+) Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Calculate expected values and use them to solve problems

Indicator: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Using Probability to Make Decisions

Standard: Calculate expected values and use them to solve problems

Indicator: (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Understand independence and conditional probability and use them to interpret data

Indicator: 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,"ť "and,"ť "not"ť).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Understand independence and conditional probability and use them to interpret data

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Understand independence and conditional probability and use them to interpret data

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Understand independence and conditional probability and use them to interpret data

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Conditional Probability and the Rules of Probability

Standard: Understand independence and conditional probability and use them to interpret data

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 3 (1 user) |

Quality of Explanation of the Subject Matter | 3 (1 user) |

Utility of Materials Designed to Support Teaching | 3 (1 user) |

Quality of Assessments | 3 (1 user) |

Quality of Technological Interactivity | 2 (1 user) |

Quality of Instructional and Practice Exercises | 2 (1 user) |

Opportunities for Deeper Learning | 2 (1 user) |

# Tags (9)

- Mathematics
- CCSS
- Common Core Math
- Common Core PD
- Conditional Probability
- ODE Learning
- Statistics and Probability
- Tree Diagrams
- adult education

## Comments