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Probability axioms

The facts that the probability

  1. of event is a non-negative real number,
    \[\forall A, \> \Pr(A) \geq 0
    \]
  2. of sample space is the unit,
    \[\Pr(\Omega) = 1
    \]
  3. of mutually exclusive events is
    \[\Pr(A_1 \cup A_2 \cup \ldots) = \Pr(A_1) + \Pr(A_2) + \cdots
    \]

    or equivalently

    \[\Pr( \bigcup_{i = 1}^{\infty} E_i ) = \sum_{i = 1}^{\infty} \Pr(E_i)
    \]

    .


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