Proving sets to be independent I know that I can use P(AB)=P(A)P(B) to prove whether sets are independent. But how can I use this to say that P(A)=0.3 and P(B)=0.4 and P(AUB)=0.6 are or aren't independent?
It's fine not to give an outright solution, an explanation would be much more helpful!

Use the fact that $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
