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Probability axioms

The basis basis of probability theory:

1. the probability of any proposition is a non-negative real number,

   \[\forall p, \> \Pr(p) \geq 0,
   \]

2. the probability of every tautology \(\tau\) is one, so

   \[\Pr(\tau) = 1,
   \]

3. for every mutually exclusive propositions \(p\) and \(q\),

   \[\Pr(p \lor q) = \Pr(p) + \Pr(q).
   \]

[9, Sec. 8.1.2]

• Proof 1: Probability of negation
• Proof 2: Probability of biconditional