Let \( \mathrm{A} \) and \( \mathrm{B} \) be two events such that \...

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Let \( \mathrm{A} \) and \( \mathrm{B} \) be two events such that \( P(\overline{A \cup B})=\frac{1}{6} \),
\( \mathrm{P} \) \( P(A \cap B)=\frac{1}{4} \) and \( P(\bar{A})=\frac{1}{4} \), where \( \bar{A} \) stands for complement of event \( \mathrm{A} \), Then the events \( \mathrm{A} \) and \( \mathrm{B} \) are
(1) independent but not equally likely
(2) independent and equally likely
(3) mutually exclusive and independent
(4) equally likely but not independent
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