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# Conditional Probability

• ### 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 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.

• ### Song: It Might Not Be That Bad

A song for use in helping students to apply Bayes Theorem and examine marginal and conditional proportions in a table to see how, for rare conditions, most positive test results may be false positives.  Lyrics and music by Tom Toce copyright 2015.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### Brilliant.org - Lessons in Probability

How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.

By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science.  This course includes 62 interactive quizzes and more than 400 probabilty-based problems with solutions.  Access to this course requires users to sign up for a free account.

• ### STatistics Education Web (STEW)

Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.

STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.