Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Elementary probability: Theory and calculations

In course

MSE-213: Probability and statistics for materials science

The course establishes the concepts of statistical analysis, probability theory, and data analysis. This includes standard statistical tests, correlation analysis and experimental design. It introduces computational statistical methods to analyse large dat ...

Description

This lecture covers elementary probability theory, including set theory operations, Laplacian probability, conditional probability, and stochastic independence. It explains concepts such as union, intersection, complement, and subset, and provides rules for probability calculations. The instructor uses examples like roulette and dice rolls to illustrate these concepts.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Mathematics

Probability theory: Topics in probability theory

Related concepts (32)

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Bayesian probability

Bayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Related lectures (50)

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Probability Basics: Theory and Applications

Covers basic probability theory, conditional probability, independence, and Bayes' Theorem.

Probability and Statistics

Introduces key concepts in probability and statistics, covering random experiments, events, intersections, unions, and more.

Probability and Statistics: Independence and Conditional Probability

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

Introduction to Probability Theory