In this lesson is colected four practical exercises about probability. Lesson is ready to use, but teachers should be prepared to add some extra information about this topic befor doing the lesson.

These practice tests from MIT OpenCourseWare cover topics in the Introductory Probability and Statistics course. They were originally written by Professors Jeremy Orloff and Jonathan Bloom, and adapted by the team at OpenStax CreatorFest. The files include both assessments and solutions.

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example:

The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of “The Ten Things Everyone Should Know About Science”.
A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions.
Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget.

The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

This course introduces students to the modeling, quantification, and analysis of uncertainty.  The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management.
Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

Lecture Videos by MIT Professor John Tsitsiklis
Lecture Slides and Readings
Recitation Problems and Solutions
Recitation Help Videos by MIT Teaching Assistants
Tutorial Problems and Solutions
Tutorial Help Videos by MIT Teaching Assistants
Problem Sets with Solutions
Exams with Solutions

Related Resource

A complementary resource, Introduction to Probability, is provided by the videos developed for an EdX version of 6.041. These videos cover more or less the same content, in somewhat different order, and in somewhat more detail than the videotaped live lectures.

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.) 

The addition rule for probability is explained using Venn Diagrams. [Probability playlist: Lesson 3 of 29]

This course covers interpretations of the concept of probability. Topics include basic probability rules; random variables and distribution functions; functions of random variables; and applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. The course also considers elements of statistics; Bayesian methods in engineering; methods for reliability and risk assessment of complex systems (event-tree and fault-tree analysis, common-cause failures, human reliability models); uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling); and an introduction to Markov models. Examples and applications are drawn from nuclear and other industries, waste repositories, and mechanical systems.

Students will begin to think about probability by considering how likely it is that their house will be struck by lightning. They will consider the relative likelihood of familiar events (e.g., outdoor temperature, test scores) on the continuum between impossible and certain. Students will discuss where on the continuum "likely," "unlikely," and "equally likely as unlikely" areGoals and Learning ObjectivesThink about the concept of likelihood.Understand that probability is a measure of likelihood.Informally estimate the likelihood of certain events.Begin to think about why one event is more likely than another.SWD: Students with disabilities may need additional support seeing the relationships among problems and strategies. Throughout this unit, keep anchor charts available and visible to assist them in making connections and working toward mastery. Provide explicit think alouds comparing strategies and making connections. In addition, ask probing questions to get students to articulate how a peer solved the problem or how one strategy or visual representation is connected or related to another.

This lesson is a birthday problem that determines the probability that at least 2 people in a room of 30 share the same birthday. [Probability playlist: Lesson 17 of 29]

This lesson presents an example of dependent probability. [Probability playlist: Lesson 10 of 29]

This lesson presents an example of dependent probability. [Probability playlist: Lesson 11 of 29]

This page of Statistical Java describes 11 different probability distributions including the Binomial, Poisson, Negative Binomial, Geometric, T, Chi-squared, Gamma, Weibull, Log-Normal, Beta, and F. Each distribution has its own applet.

This lesson begins a six part series of basic probabiltiy using module examples. [Probability playlist: Lesson 4 of 29]

This lesson demonstrates probability using combinations and shows the probability of getting exatly 3 heads in 8 flips of a fair coin. [Probability playlist: Lesson 14 of 29]

This lesson is another demonstration of probability and combinations to determine the probability of making at least 3 out of 5 basketball free throws. [Probability playlist: Lesson 15 of 29]

This lesson uses playing cards and Venn Diagrams to explain the idea of probability [Probability playlist: Lesson 2 of 29]