PS.SPCR: Conditional Probability and Rules of Probability

PS.SPCR.1: Describe events as subsets of a sample space and

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

PS.SPCR.1.a: Use Venn diagrams to represent intersections, unions, and complements.

Compound Inequalities

PS.SPCR.1.b: Relate intersections, unions, and complements to the words and, or, and not.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

PS.SPCR.1.c: Represent sample spaces for compound events using Venn diagrams.

Independent and Dependent Events
Permutations and Combinations

PS.SPCR.2: Use the multiplication rule to calculate probabilities for independent and dependent events. 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.

Independent and Dependent Events

PS.SPCR.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.

Independent and Dependent Events

PS.SPCR.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.

Histograms

PS.SPCR.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

PS.SPCR.6: Calculate the conditional probability of an event A given event B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Independent and Dependent Events

PS.SPCR.7: Apply the Addition Rule and the Multiplication Rule to determine probabilities, including conditional probabilities, and interpret the results in terms of the probability model.

Independent and Dependent Events

PS.SPCR.8: Use permutations and combinations to solve mathematical and real-world problems, including determining probabilities of compound events. Justify the results.

Binomial Probabilities
Permutations and Combinations

PS.SPMJ: Making Inferences and Justifying Conclusions

PS.SPMJ.1: Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population.

Polling: City
Polling: Neighborhood
Populations and Samples

PS.SPMJ.2: Distinguish between experimental and theoretical probabilities. Collect data on a chance event and use the relative frequency to estimate the theoretical probability of that event. Determine whether a given probability model is consistent with experimental results.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

PS.SPMJ.3: Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods to reduce bias.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood

PS.SPMJ.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Polling: City
Polling: Neighborhood

PS.SPMJ.6: Evaluate claims and conclusions in published reports or articles based on data by analyzing study design and the collection, analysis, and display of the data.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples
Real-Time Histogram

PS.SPID: Interpreting Data

PS.SPID.1: Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers.

Box-and-Whisker Plots
Correlation
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

PS.SPID.2: Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions

PS.SPID.3: Summarize and represent data from a single data set. Interpret differences in shape, center, and spread in the context of the data set, accounting for possible effects of extreme data points (outliers).

Box-and-Whisker Plots
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

PS.SPID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Polling: City
Populations and Samples
Real-Time Histogram

PS.SPID.5: Analyze bivariate categorical data using two-way tables and identify possible associations between the two categories using marginal, joint, and conditional frequencies.

Histograms

PS.SPID.6: Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

PS.SPID.7: Find linear models using median fit and regression methods to make predictions. Interpret the slope and intercept of a linear model in the context of the data.

Cat and Mouse (Modeling with Linear Systems)
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

PS.SPID.8: Compute using technology and interpret the correlation coefficient of a linear fit.

Correlation

PS.SPID.9: Differentiate between correlation and causation when describing the relationship between two variables. Identify potential lurking variables which may explain an association between two variables.

Correlation

PS.SPID.10: Create residual plots and analyze those plots to compare the fit of linear, quadratic, and exponential models to a given data set. Select the appropriate model and use it for interpolation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

PS.SPMD: Using Probability to Make Decisions

PS.SPMD.1: Develop the probability distribution for a random variable defined for a sample space in which a theoretical probability can be calculated and graph the distribution.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

PS.SPMD.2: Calculate the expected value of a random variable as the mean of its probability distribution. Find expected values by assigning probabilities to payoff values. Use expected values to evaluate and compare strategies in real-world scenarios.

Binomial Probabilities
Lucky Duck (Expected Value)
Polling: City

PS.SPMD.3: Construct and compare theoretical and experimental probability distributions and use those distributions to find expected values.

Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

PS.SPMD.4: Use probability to evaluate outcomes of decisions by finding expected values and determine if decisions are fair.

Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

PS.SPMD.5: Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions.

Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

PS.SPMD.6: Analyze decisions and strategies using probability concepts.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability