In: Statistics and Probability
Derive below Results 1 to 4 from Axioms 1 to 3 given in Section 2.1.2 in the textbook.
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).