In a group, P(A)=0.5P(A) = 0.5P(A)=0.5, P(B)=0.3P(B) = 0.3P(B)=0.3, and P(A∩B)=0.15P(A \cap B) = 0.15P(A∩B)=0.15. Are A and B independent?
Yes, because P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times 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)=P(A)P(A|B) = P(A)P(A∣B)=P(A).
No, because P(A∣B)=0P(A|B) = 0P(A∣B)=0.