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# Event A and B are such that $P(A) = \frac{1}{2}, P(B) = \frac{7}{12}$, P (not A or not B) =$\frac{1}{4}$. State whether A and B are independent.

P(not A or not B) = $\frac{1}{4}$
$\implies P(\bar{A} \cup \bar{B}) = P(\bar {A \cap B}) = \frac{1}{4}$
$\therefore P(A \cap B) = 1 - \frac{1}{4} = \frac{3}{4}$
$P(A \cap B) \neq P(A) P(B)$