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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 that updates the probability of an event based on new evidence or information.
  • Numerator
    The top part of a probability fraction, often representing joint or combined probabilities.
  • Denominator
    The bottom part of a probability fraction, typically representing the total or given probability.
  • Joint Probability
    The chance that two events occur together, often used in the calculation of conditional probabilities.
  • Complement
    The event representing all outcomes not included in a specific event, such as not drawing from a certain bag.
  • Event A
    The known or given outcome in a probability scenario, such as drawing a red marble.
  • Event B
    The outcome of interest in a probability scenario, such as selecting from a specific bag.
  • B Complement
    The scenario where the outcome of interest does not occur, such as not selecting from the left bag.
  • Probability Fraction
    A ratio expressing the likelihood of an event, with a numerator and denominator representing different probabilities.
  • Given Event
    The condition or information already known when calculating conditional probabilities.
  • Prior Probability
    The initial likelihood of an event before considering new evidence or information.
  • Posterior Probability
    The updated likelihood of an event after incorporating new evidence using Bayes' theorem.
  • Sample Space
    The set of all possible outcomes in a probability experiment, such as all marbles in both bags.
  • Fraction Simplification
    The process of reducing probability ratios to their simplest form for easier interpretation.