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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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