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Probability definitions

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  • Theoretical Probability
    Calculated using possible outcomes before any experiment, found by dividing favorable outcomes by total possible outcomes.
  • Empirical Probability
    Calculated from actual experimental data, found by dividing the number of times an event occurs by the total number of trials.
  • Sample Space
    Set of all possible outcomes for a random experiment, often represented using curly brackets in set notation.
  • Event
    Any outcome or group of outcomes from a random experiment, regardless of size or significance.
  • Complement
    All outcomes in the sample space where a specific event does not occur; its probability is 1 minus the event's probability.
  • Mutually Exclusive Events
    Events that cannot occur at the same time; their probabilities are added to find the chance of either occurring.
  • Non-Mutually Exclusive Events
    Events that can occur simultaneously; their combined probability requires subtracting the overlap.
  • Independent Events
    Events where the outcome of one does not affect the outcome of the other; their joint probability is the product of their probabilities.
  • Dependent Events
    Events where the outcome of one affects the probability of the other occurring.
  • Set Notation
    Mathematical symbols and brackets used to represent collections of outcomes, such as events or sample spaces.
  • Or Probability
    Probability that at least one of multiple events occurs; calculated differently for mutually exclusive and non-mutually exclusive events.
  • And Probability
    Probability that multiple events all occur; for independent events, found by multiplying their individual probabilities.
  • Overlap Region
    Portion in a Venn diagram where two events share outcomes, relevant for non-mutually exclusive events.
  • Trial
    A single occurrence or observation in an experiment, used to gather data for empirical probability.
  • Favorable Outcome
    An outcome that satisfies the condition of the event being considered in a probability calculation.