# 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!

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

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So since 0.6=0.3+0.4-.12 gives 0.6=0.58 which is false, they aren't independent? –  user7174 Feb 17 '11 at 0:55
Yes, that would be one way of saying it (you're assuming they're independent and you're arriving at a contradiction). –  Weltschmerz Feb 17 '11 at 1:08
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. –  user7174 Feb 17 '11 at 1:13