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  2. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...

  3. Game of chance - Wikipedia

    en.wikipedia.org/wiki/Game_of_chance

    Roulette is a game of pure chance; no strategy can give players advantages, the outcome is determined purely by which numbered pocket a ball randomly falls into.. A game of chance is in contrast with a game of skill.

  4. Random permutation statistics - Wikipedia

    en.wikipedia.org/wiki/Random_permutation_statistics

    This average parameter represents the probability that if we again select a random element of [] of a random permutation, the element lies on a cycle of size m. The function b ( k ) {\displaystyle b(k)} is equal to m {\displaystyle m} for m = k {\displaystyle m=k} and zero otherwise, because only cycles of length m contribute, namely m elements ...

  5. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.

  6. Bernoulli distribution - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_distribution

    In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, [1] is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability =.

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  8. Random permutation - Wikipedia

    en.wikipedia.org/wiki/Random_permutation

    A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...

  9. Random graph - Wikipedia

    en.wikipedia.org/wiki/Random_graph

    The probability of an edge uv between any vertices u and v is some function of the dot product u • v of their respective vectors. The network probability matrix models random graphs through edge probabilities, which represent the probability , that a given edge , exists for a specified time period. This model is extensible to directed and ...