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Bayes' Theorem definitions

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  • Conditional Probability
    Likelihood of an event occurring when another event is already known to have happened.
  • Bayes' Theorem
    A formula relating the probability of two events, simplifying calculation of conditional probabilities.
  • Numerator
    The top part of a fraction in Bayes' Theorem, representing the joint probability of two events.
  • Denominator
    The bottom part of a fraction in Bayes' Theorem, representing the probability of the given event.
  • Joint Probability
    Chance that two events occur together, used in the numerator of Bayes' Theorem.
  • Complement
    The event representing all outcomes not included in a specified event, such as not drawing from a particular bag.
  • Event
    A specific outcome or set of outcomes, such as drawing a red marble or selecting a particular bag.
  • Probability
    A numerical measure of how likely an event is to occur, expressed as a fraction or percentage.
  • Fraction
    A mathematical expression used to represent probabilities, with a numerator and denominator.
  • Given Event
    The condition or outcome already known, which influences the calculation of conditional probability.
  • Red Marble
    An outcome used to illustrate conditional probability, representing a specific event in the example.
  • Left Bag
    A category in the example, used to determine probabilities based on marble selection.
  • Right Bag
    An alternative category in the example, representing the complement of the left bag event.
  • Practice
    Repeated exercises or examples to reinforce understanding and application of Bayes' Theorem.
  • Simplification
    The process of reducing complex probability expressions to more manageable forms for calculation.