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Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE?

1. $P(A \cap B) = P(A)P(B)$
2. $P(A \mid B) = P(A)$
3. $P(A \cup B) = P(A) + P(B)$
4. $P(\overline{A} \cap \overline{B} )= P(\overline{A})P(\overline{B})$