Consider two events AAA and BBB where P(A)=0.3,P(B)=0.5P(A) = 0.3, P(B) = 0.5P(A)=0.3,P(B)=0.5, and P(A∪B)=0.65P(A \cup B) = 0.65P(A∪B)=0.65. Are events AAA and BBB independent?
Yes, because P(A)+P(B)=P(A∪B)P(A) + P(B) = P(A \cup B)P(A)+P(B)=P(A∪B).
No, because P(A)P(B)≠P(A∩B)P(A)P(B) \neq P(A \cap B)P(A)P(B)=P(A∩B).
Yes, because P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B)P(A∩B)=P(A)P(B).
Cannot be determined.