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Derive below Results 1 to 4 from Axioms 1 to 3. Axiom 1: P(A)≥ 0 Axiom...

Derive below Results 1 to 4 from Axioms 1 to 3.

Axiom 1: P(A)≥ 0

Axiom 2: P(S)=1

Axiom 3: If A and B are mutually exclusive events, then P(A ∪ B)= P(A)+P(B)

Result 1: P(Ac)=1−P(A)

Result 2: For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B)

Result 3: For any two events A and B, P(A) = P(A ∩ B) + P(A ∩ Bc)

Result 4: If B ⊂ A, then A ∩ B = B. Therefore, P(A) − P(B) = P(A ∩ Bc), and P(A) ? P(B).

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orchestra answered 2 years ago
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