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  2. Hypergeometric distribution - Wikipedia

    en.wikipedia.org/wiki/Hypergeometric_distribution

    In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.

  3. Urn problem - Wikipedia

    en.wikipedia.org/wiki/Urn_problem

    Two urns containing white and red balls. In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container.

  4. Problem of points - Wikipedia

    en.wikipedia.org/wiki/Problem_of_points

    The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.

  5. Probability theory - Wikipedia

    en.wikipedia.org/wiki/Probability_theory

    This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.

  6. Rule of succession - Wikipedia

    en.wikipedia.org/wiki/Rule_of_succession

    In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. [1] The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at all in (finite) sample data.

  7. Outline of probability - Wikipedia

    en.wikipedia.org/wiki/Outline_of_probability

    The certainty that is adopted can be described in terms of a numerical measure, and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty) is called the probability. Probability theory is used extensively in statistics , mathematics , science and philosophy to draw conclusions about the likelihood of potential ...

  8. Axiom of choice - Wikipedia

    en.wikipedia.org/wiki/Axiom_of_choice

    Then the set X = {{x 1, y 1}, {x 2, y 2}, {x 3, y 3}, ...} can be in the model but sets such as {x 1, x 2, x 3, ...} cannot, and thus X cannot have a choice function. In 1938, [ 19 ] Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe ) that satisfies ZFC ...

  9. Exchangeable random variables - Wikipedia

    en.wikipedia.org/wiki/Exchangeable_random_variables

    The von Neumann extractor is a randomness extractor that depends on exchangeability: it gives a method to take an exchangeable sequence of 0s and 1s (Bernoulli trials), with some probability p of 0 and = of 1, and produce a (shorter) exchangeable sequence of 0s and 1s with probability 1/2.