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Probability definitions

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  • Probability
    A numerical measure expressing the likelihood of an event, ranging from 0 (impossible) to 1 (certain).
  • Event
    A specific outcome or set of outcomes from a random process, such as rolling a die or drawing a card.
  • Theoretical Probability
    A ratio based on possible outcomes, calculated before any experiment is performed.
  • Empirical Probability
    A ratio based on actual results from experiments or collected data, reflecting observed frequencies.
  • Sample Space
    A set containing all possible outcomes of a random experiment, often shown in curly brackets.
  • Complement
    All outcomes in the sample space that are not part of a specified event.
  • Mutually Exclusive Events
    Events that cannot occur at the same time; their occurrence is completely separate.
  • Non-Mutually Exclusive Events
    Events that can occur simultaneously, sharing some overlapping outcomes.
  • Independent Events
    Events where the outcome of one does not affect the outcome of the other.
  • Dependent Events
    Events where the outcome of one influences the outcome of the other.
  • Addition Rule
    A method for finding the probability of at least one of multiple events, adjusted for overlap if needed.
  • Multiplication Rule
    A method for finding the probability of multiple independent events all occurring, by multiplying their probabilities.
  • Set Notation
    A mathematical way to represent collections of outcomes, often using symbols like U (union) and ∩ (intersection).
  • Union
    The set of outcomes that belong to at least one of two events, represented by the symbol U.
  • Intersection
    The set of outcomes shared by two events, represented by the symbol ∩.