Probability
Counting Applications worksheets
Choose among the multiplication principle, ordered selections without replacement, and unordered combinations in varied finite contexts.
Preview and downloadModel chance. Reason from data.
Introductory probability and statistics worksheets
Prepare a sequence of original worksheets that connects probability models to conclusions from data. Choose individual skills or assemble an editable packet for a lesson, tutorial or review.
44 printable resources with separate worked answer pages.
Choose a topicChoose a starting point
Use algebra, functions, sums, derivatives and basic definite integrals. Review sample variance and z-scores before inference. Teachers can select calculator-supported tasks or supplied numerical references as each worksheet allows.
Review sample variance · Review z-scores · Review sets and Venn diagrams · Review calculus
Step 1
Count outcomes and condition on evidence
Choose a sample space, reconstruct overlapping counts and keep the direction of every conditional probability clear.
Probability
Compound Counting and Probability worksheets
Reconstruct two- and three-set totals, count compound outcomes, and calculate collision probabilities by complements.
Preview and download
Probability
Conditional Probability worksheets
Compare conditional and joint probabilities using complete two-way count tables and two sequential draws without replacement.
Preview and download
Probability
Total Probability and Bayes' Theorem worksheets
Practice forward total probability and reverse conditional probability with explicit two- and three-source partitions.
Preview and download
Probability
Independence and Base Rates worksheets
Check independence in rational tables and compare Bayesian posteriors under different priors.
Preview and downloadStep 2
Describe a discrete random variable
Move from a PMF to its CDF, quantiles and moments. Choose a model from the experiment and state its assumptions.
Probability
Discrete Probability Distributions worksheets
Use valid finite probability tables to find missing entries, event probabilities, expected value, and population variance.
Preview and download
Probability
Discrete CDFs, Transformations, and Moments worksheets
Build step CDFs, find quantiles, merge transformed PMFs, and apply weighted moment rules.
Preview and download
Probability
Bernoulli and Normal Model Selection worksheets
Distinguish Bernoulli from binomial counts and identify normal support, PDF parameters, variance, and standard deviation.
Preview and download
Probability
Binomial Distribution worksheets
Calculate exact, at-most, and at-least binomial probabilities plus mean and variance for bounded trial counts.
Preview and download
Probability
Geometric Distribution worksheets
Model the number of trials through the first success using exact, cumulative, tail, mean, and variance questions.
Preview and download
Probability
Poisson Distribution worksheets
Scale a constant event rate to an exposure, then calculate exact, cumulative, tail, mean, and variance results for Poisson counts.
Preview and downloadStep 3
Connect continuous density and probability
Probability is area. Include support boundaries, normalize the density and account for every preimage when transforming a variable.
Probability
Continuous PDFs and CDFs worksheets
Normalize bounded polynomial densities, integrate probabilities and moments, build piecewise CDFs, recover PDFs, and invert CDFs for quantiles.
Preview and download
Probability
Uniform Distribution worksheets
Use support length for density, clipped interval and conditional probabilities, piecewise CDFs, quantiles, mean, and variance.
Preview and download
Probability
Exponential Distribution worksheets
Work with exponential waiting-time CDFs, survival probabilities, intervals, quantiles, moments, rate-mean conversion, and memorylessness.
Preview and download
Statistics
Normal Distribution worksheets
Standardize normal values, find below, above, and between probabilities, and invert the model for percentiles and central intervals.
Preview and download
Probability
Continuous Random Variable Transformations worksheets
Transform supports, CDFs, and PDFs for affine, square, square-root, and two-preimage mappings.
Preview and downloadStep 4
Combine variables and study sample averages
Derive marginals and conditional distributions, calculate covariance, and distinguish LLN concentration from a CLT approximation.
Probability
Joint Discrete Distributions worksheets
Use numeric joint PMF tables for CDFs, events, marginals, conditionals, moments, and independence.
Preview and download
Probability
Joint Continuous Distributions worksheets
Integrate densities on rectangular and triangular supports for probabilities, CDFs, marginals, conditionals, and independence.
Preview and download
Probability
Covariance of Random Variables worksheets
Calculate covariance and correlation from joint PMFs or paired data with explicit denominators.
Preview and download
Probability
Density Histograms and the LLN worksheets
Convert unequal-width bin counts to density and area, then interpret supplied repeated-sampling summaries.
Preview and download
Probability
Sampling Distributions and the CLT worksheets
Find moments and probabilities for means and sums, distinguish exact normal results from CLT approximations, and use continuity correction.
Preview and downloadStep 5
Learn about parameters from data
Separate a parameter from a statistic, compare likelihoods, update prior information and interpret posterior prediction and credible intervals.
Statistics
Parameters, Statistics, and Inference worksheets
Classify study stages, identify observations and parameters, reject invalid statistics, and compute sample summaries.
Preview and download
Statistics
Likelihood and MLE worksheets
Write and compare likelihoods, find bounded analytic MLEs, and handle normal variance and support-dependent uniform endpoints.
Preview and download
Statistics
Discrete Bayesian Updating worksheets
Complete prior-likelihood-posterior tables, compare sequential and batch evidence, and handle zero priors or impossible evidence.
Preview and download
Statistics
Bayesian Prediction and Odds worksheets
Form predictive mixtures, convert odds and probability, update odds with Bayes factors, and interpret evidence direction.
Preview and download
Statistics
Continuous-Prior Bayesian Updating worksheets
Normalize polynomial prior-likelihood products, integrate evidence, predict future outcomes, and distinguish density from point mass.
Preview and download
Statistics
Beta Conjugate Priors worksheets
Normalize integer-shape Beta densities, interpret strength, update Bernoulli/binomial/geometric data, and predict.
Preview and download
Statistics
Normal Conjugate Priors worksheets
Update a normal mean with known observation variance using precision weights and verify sequential consistency.
Preview and download
Statistics
Prior Choice and Sensitivity worksheets
Compare priors under identical data, contrast weak and strong priors, preserve zero prior mass, and justify prior choices.
Preview and download
Statistics
Credible Intervals worksheets
Calculate discrete and continuous posterior interval mass, equal-tail intervals, interpretations, and quantile-based prior choices.
Preview and downloadStep 6
Evaluate evidence with a stated test
Specify hypotheses, assumptions and an extremeness rule before calculating. Keep p-values, error rates and posterior probabilities distinct.
Statistics
Hypothesis Tests, Errors, and Power worksheets
Design null and alternative hypotheses, choose rejection sets, and compute Type I error, Type II error, and power.
Preview and download
Statistics
Exact Binomial and Known-Sigma z Test worksheets
Run exact one- and two-sided binomial tests and known-sigma z tests from raw data or summaries.
Preview and download
Statistics
One-Sample, Paired, Pooled, and Welch t Test worksheets
Select and run one-sample, paired, equal-variance pooled, and unequal-variance Welch t tests.
Preview and download
Statistics
Chi-Square Goodness-of-Fit and Independence worksheets
Build expected counts and calculate Pearson X2 or likelihood-ratio G for categorical data.
Preview and download
Statistics
One-Way ANOVA worksheets
Compute between and within sums of squares, complete ANOVA tables, and interpret omnibus F tests.
Preview and download
Statistics
Bayesian Claims versus NHST Claims worksheets
Compare p-values, error rates, and posterior hypothesis probabilities without reversing their conditioning.
Preview and downloadStep 7
Quantify uncertainty in an estimate
Use a sampling model or a clearly specified resampling procedure. Interpret repeated-sample coverage and the limits of small classroom bootstrap examples.
Statistics
Normal-Data Confidence Intervals worksheets
Construct z and t mean intervals, chi-square variance intervals, inspect coverage, and invert a two-sided test.
Preview and download
Statistics
Large-Sample Confidence Intervals worksheets
Use conservative proportion bounds, the approximate 95% rule, and CLT intervals for general means.
Preview and download
Statistics
Bootstrap Confidence Intervals worksheets
Build empirical PMFs, calculate supplied resample statistics, and form percentile and basic bootstrap intervals.
Preview and downloadStep 8
Fit, interpret and question a regression model
Inspect paired data, calculate residuals and error, compare model complexity and interpret each predictor while holding the others fixed.
Statistics
Scatterplots and Correlation worksheets
Construct and read labeled scatterplots from actual paired observations, calculate Pearson r, and interpret linear association without claiming causation.
Preview and download
Statistics
Linear Regression and Residuals worksheets
Fit ordinary least-squares lines with intercepts, predict responses, calculate observed-minus-predicted residuals, and identify extrapolation.
Preview and download
Statistics
Least-Squares Curve Models worksheets
Compare supplied line, quadratic, cubic, and transformed exponential models using residuals and SSE.
Preview and download
Statistics
Regression Model Diagnostics worksheets
Read finite residual plots, compare held-out errors, assess influential points, and reason about regression to the mean.
Preview and download
Statistics
Multiple Regression Introduction worksheets
Use a supplied two-predictor equation to identify variables, predict, calculate residuals and SSE, and write the least-squares objective.
Preview and downloadPrepare a learning packet
Start with complete worksheets, then remove or reorder them. Choose Letter or A4 and a student or teacher edition.
Continuous probability packet
Connect density and cumulative probability with uniform, exponential and normal models. Each worksheet has its own worked answer pages.
Edit this packet →Counts and waiting times packet
Compare binomial and Poisson counts with geometric and exponential waiting models. State the assumptions and units for each.
Edit this packet →Joint distributions and sampling packet
Move from joint tables and densities to covariance, density histograms and the sampling distribution of a mean.
Edit this packet →Random variable foundations packet
Connect compound counting and independence with model selection, discrete CDFs and continuous transformations.
Edit this packet →Likelihood and Bayesian updating packet
Connect parameters, likelihood, discrete updates and posterior prediction.
Edit this packet →Priors and posterior uncertainty packet
Work through continuous priors, beta and normal updates, sensitivity and credible intervals.
Edit this packet →Hypothesis testing packet
Choose a test design, calculate evidence and interpret the conclusion across common data types.
Edit this packet →Intervals and bootstrap packet
Compare normal-model, large-sample and bootstrap uncertainty calculations.
Edit this packet →Regression models packet
Extend straight-line fitting to transformed curves, diagnostics and multiple predictors.
Edit this packet →Keep the assumptions with the answer
Match the calculation to the experiment. Independence, a sampling model and a prior each express different assumptions. Label approximations, keep units visible and explain what the final number means.
These are paper mathematics exercises with worked keys. They support introductory college study; they do not replace a full course, software labs or assessment by an instructor.
Explore all probability worksheets · Explore all statistics worksheets