Let AAA and BBB be two events with P(A)=0.5P(A) = 0.5P(A)=0.5 and P(B)=0.4P(B) = 0.4P(B)=0.4. If 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)≠P(A)P(B)P(A \cap B) \neq P(A)P(B)P(A∩B)=P(A)P(B)
Yes, because P(A∣B)=1P(A|B) = 1P(A∣B)=1
No, because they are mutually exclusive