Experiment with independent events and find how often certain results occur!

**Grades covered:**3 through 12

**Curriculum Topics:**Probability, Independent Events, Compound Probability

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 4||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 5||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “”The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.”” “”For every vote candidate A received, candidate C received nearly three votes.””||Common Core Mathematics||Grade 6||Ratios And Proportional Relationships||Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems|||6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.||Common Core Mathematics||Grade 6||Ratios And Proportional Relationships||Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems|||6.SP.5.a. Reporting the number of observations.||Common Core Mathematics||Grade 6||Statistics And Probability||Summarize And Describe Distributions|||6.SP.5.b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.||Common Core Mathematics||Grade 6||Statistics And Probability||Summarize And Describe Distributions|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.||Common Core Mathematics||Grade 7||Statistics And Probability||Use Random Sampling To Draw Inferences About A Population|||7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||7.SP.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?||Common Core Mathematics||Grade 8||Statistics And Probability||Investigate Patterns Of Association In Bivariate Data|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices|||HS.S.CP.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.||Common Core Mathematics||High School||Conditional Probability And The Rules Of Probability||Understand Independence And Conditional Probability And Use Them To Interpret Data|||HS.S.CP.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.||Common Core Mathematics||High School||Conditional Probability And The Rules Of Probability||Understand Independence And Conditional Probability And Use Them To Interpret Data

1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions.||CA Mathematics||Grade 3||04. Statistics, Data Analysis, and Probability|||2.0 Students make predictions for simple probability situations.||CA Mathematics||Grade 4||04. Statistics, Data Analysis, and Probability|||3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.||CA Mathematics||Grade 6||04. Statistics, Data Analysis, and Probability|||1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.||CA Mathematics||Grade 8 – 12||04. Probability and Statistics

**Categories include:**

- Grades 3-5
- Grades 6-8
- Math

**Tags:**Ratios & Proportions, Probability

**Subjects covered:**["Math"]