### PS.SPCR: Conditional Probability and Rules of Probability

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

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

Compound Inequalities

#### 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

#### 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.

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

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

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

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

#### 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)

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

#### 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.

Correlation

Solving Using Trend Lines

#### 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

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.

Geometric Probability

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

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

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.

Probability Simulations

Theoretical and Experimental Probability

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

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

Correlation last revised: 4/4/2018