In this study, we examined participants' choice behavior in a sequential risk-taking task. We were especially interested in the extent to which participants focus on the immediate next choice or consider the entire choice sequence. To do so, we inspected whether decisions were either based on conditional probabilities (e.g., being successful on the immediate next trial) or on conjunctive probabilities (of being successful several times in a row). The results of five experiments with a simplified nine-card Columbia Card Task and a CPT-model analysis show that participants' choice behavior can be described best by a mixture of the two probability types. Specifically, for their first choice, the participants relied on conditional probabilities, whereas subsequent choices were based on conjunctive probabilities. This strategy occurred across different start conditions in which more or less cards were already presented face up. Consequently, the proportion of risky choices was substantially higher when participants started from a state with some cards facing up, compared with when they arrived at that state starting from the very beginning. The results, alternative accounts, and implications are discussed.

This is a brief conditional probability examplediscussing probabilities like P(A | B) using breakfast and lunch as examples.

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.

This lesson combines conditional probability and combinations to determine the probability of picking a fair coin given that it flipped 4 out of 6 heads. [Probability playlist: Lesson 16 of 29]

This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, and limit theorems. There is also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; and deeper understanding of conditional distributions and expectations.

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.

In this module, students build on their understanding of probability developed in previous grades.  In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent.  Students are also introduced to three techniques for counting outcomes.  Topic B presents information related to random variables and discrete probability distributions.  Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En este módulo, los estudiantes se basan en su comprensión de la probabilidad desarrollada en calificaciones anteriores. En el tema A, la regla de multiplicación para eventos independientes introducidos en el álgebra II se generaliza a una regla que puede usarse para calcular la probabilidad donde dos eventos no son independientes. Los estudiantes también se introducen a tres técnicas para contar los resultados. El tema B presenta información relacionada con variables aleatorias y distribuciones de probabilidad discretas. El Tema C es un tema Capstone para este módulo, donde los estudiantes usan lo que han aprendido sobre la probabilidad y el valor esperado para analizar estrategias y tomar decisiones en una variedad de contextos.

English Description:
In this module, students build on their understanding of probability developed in previous grades.  In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent.  Students are also introduced to three techniques for counting outcomes.  Topic B presents information related to random variables and discrete probability distributions.  Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts.

In this class, students will be able to identify what is probability and have a general concept. The students should be able to calculate the probability questions by using the formula of conditional probability (P( A|B )=number of A/the total number of outcomes.) 

A work in progress, this FlexBook is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.

CK-12 Foundation's Basic Probability and Statistics - A Short Course is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.

This site teaches High Schoolers Conditional Probability & the Rules of Probability through a series of 1350 questions and interactive activities aligned to 11 Common Core mathematics skills.

Bayes' Theorem is a powerful tool, but what does it really mean and when is it needed? In general, students are told to use it whenever there us a priori information, and use the formula P[A|B] = P[B]XP[A|B]/P[B]
But what does that formula actually mean? To understand Bayes’ Theorem, it is necessary to first understand marginal probability tables. These tables hold the key to understanding the data.
In this paper, west coast termites provide an example of how to look at the data, how to put it together in a marginal probability table, how to ensure the data is input correctly, what are the meanings of false positive and false negative, and -- last -- how to calculate probabilities. Appendix 5 contains a medical application, based on data from the US CDC. Some of the claims made about west coast termites, such as x-ray tests and vinegar tests, may not be based on solid scientific proof. But the termites do make a good example.