Basic Probability Notation

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 In probability theory, there are several notations used to represent different aspects of probability. The most basic notation is:

  • P(A): the probability of event A occurring.

Other commonly used notations include:

  • P(A | B): the conditional probability of event A occurring, given that event B has occurred.
  • P(A, B): the joint probability of both event A and event B occurring.
  • P(A ∪ B): the probability of either event A or event B occurring (the union of A and B).
  • P(A ∩ B): the probability of both event A and event B occurring (the intersection of A and B).
  • P(A') or P(~A): the probability of event A not occurring (the complement of A).

In addition to these basic notations, there are several rules and formulas in probability theory that are used to calculate and manipulate probabilities, including:

  • Bayes' theorem: a formula for calculating conditional probabilities in terms of prior probabilities and new evidence.
  • The product rule: a formula for calculating the joint probability of multiple events.
  • The sum rule: a formula for calculating the probability of the union of multiple events.
  • The law of total probability: a formula for calculating the probability of an event in terms of conditional probabilities.
  • The expected value: a measure of the average value of a random variable over many trials.
  • The variance: a measure of the spread or variability of a random variable

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