Event Independent from Itself When Probability 0 or 1 Theorem An event A from a probability space Ω is independent from itself if and only if eitherP(A)=0orP(A)=1. ProofP(A∩A)=P(A)⋅P(A)⟹P(A)=P(A)2⟹P(A)2−P(A)=0⟹P(A)(P(A)−1)=0⟹P(A)=0orP(A)=1