If P(A)=0.4,P(B)=0.5P(A) = 0.4, P(B) = 0.5P(A)=0.4,P(B)=0.5 and P(A∪B)=0.7P(A \cup B) = 0.7P(A∪B)=0.7, are AAA and BBB independent?
Yes, because P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B)P(A∩B)=P(A)P(B)
No, because P(A∩B)=0.2≠0.2P(A \cap B) = 0.2 \neq 0.2P(A∩B)=0.2=0.2
No, because P(A∩B)=0.2P(A \cap B) = 0.2P(A∩B)=0.2 and P(A)P(B)=0.2P(A)P(B) = 0.2P(A)P(B)=0.2
Yes, because P(A∩B)=0.2P(A \cap B) = 0.2P(A∩B)=0.2