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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!

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

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    Oh, I see. Solving for P(AUB) gives 0.1, and since P(A)P(B)=0.12, which isn't 0.1, they're independent.2011-02-17