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# Elementary Probability

• ### Cartoon: Launch Risk

A cartoon suitable for use in teaching about risks and the problem with making post hoc comparisons. The cartoon is number 2107 (February, 2019) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

• ### Cartoon: Feathered Dinosaur Venn Diagram

A cartoon suitable for use in teaching about Venn Diagrams and the meaning of mutually exclusive events. The cartoon is number 2090 (December, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

• ### Food: The Probability of a Kiss

Summary: Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These concepts are developed with activities using Hershey KissesTM and may be extended to introduce the sampling distribution of a sample proportion. The activities are described in M. Richardson and S. Haller. (2002), “What is the Probability of a Kiss? (It's Not What You Think),” Journal of Statistics Education, 10(3), https://www.tandfonline.com/doi/full/10.1080/10691898.2002.11910683

Specifics: The main activity uses Hershey’s Kisses to explore the concept of probability. Three specific sub-activities are performed such as:

1. Students explore the empirical probability that a plain Hershey’s Kiss will land on its flat base when spilled from a cup.
2. Students make predictions about the probability of an almond Hershey’s Kisses landing on its base when spilled from a cup, after having experimented with the plain Kisses.
3. Students explore the properties of the distribution of a sample proportion to see whether the percentages of base landings have a specified distribution and whether they think that the number of Kisses tossed affects the shape or the mean and standard deviation of this distribution.

(Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

• ### Joke: Inequality Language

A joke about the meaning of an inequality symbol like ≤ written in February 2020 by Larry Lesser from The University of Texas at El Paso and Dennis Pearl from Penn State University.

• ### Cartoon: Modified Bayes Theorem

A cartoon suitable for use in teaching about Bayes Theorem (an obvious follow-up exercise is to ask what “P(C)” would have to be to make the “Modified Bayes Theorem” correct). The cartoon is number 2059 (October, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

• ### Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners

Probabilistic Risk Assessment (PRA) is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in complex technological systems for the purpose of cost-effectively improving their safety and performance. NASA’s objective is to better understand and effectively manage risk, and thus more effectively ensure mission and programmatic success, and to achieve and maintain high safety standards at NASA. This PRA Procedures Guide, in the present second edition, is neither a textbook nor an exhaustive sourcebook of PRA methods and techniques. It provides a set of recommended procedures, based on the experience of the authors, that are applicable to different levels and types of PRA that are performed for aerospace applications.

• ### Statistics: Basic Concepts for Astronomers

This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA.

• ### Collection: Calculators

Our online calculators and converters can help you in many daily tasks that require calculations to complete.

• ### Collection: Statistical Calculators

Free statistical calculators online.  Our basic statistical calculators will help you in common tasks you might encounter and deal mostly with simple distributions.

• ### Log-linear Models for Multidimensional Contingency Tables

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: partial/conditional tables, confounding, types of independence (mutual, joint, marginal, and conditional), identifiability constraints, partial odds ratios, hierarchical log-linear model, pairwise interaction log-linear model, conditional independence log-linear model, goodness of fit, and model building.