Probability Axioms - Axioms of Probability Axiom 1. P[ A] 0...

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1 Axioms of Probability Axiom 1. [] 0 P A for any event A S ≥⊂ Axiom 2. [] 1 PS = Axiom 3 If : that is, A and B are disjoint (or non-overlapping), [ ] AB PA B PA PB φ = = +
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2 Probability – Properties 1) Complement [ ] 1 [] c PA = 2) Union of finite number of mutually exclusive (disjoint) events 1 1 [ ] n n ii i i P A = = = 3) Subset [ ] B A PA B PA PB ⊂⇒ = 4) Union [ ] [ ] PA B PA PB PA B =+− 
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3 Proof: Subset Let .P r [ ] [] . B A ovePA B PA PB −= () , . [ ] [ ] [ ] A A B B and the two sets A B and B are mutually exclusive
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Probability Axioms - Axioms of Probability Axiom 1. P[ A] 0...

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