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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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