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If two events, $A$ and $B$, are independent, then which of the following statements is false?

Knowing whether or not event $A$ occurs does not alter the probability that event $B$ will occur.

$p\left( A \text{ and } B \right) =p(A)\cdot p(B)-p(A \text{ or } B)$

$p\left( A|B \right) =p\left( A \right)$

$p\left( B|A \right) =p\left( B \right)$

$p\left(A \text{ and } B \right) =p(A)\cdot p(B)$