jee-main 2014 Q90

jee-main · India · 06apr Independent Events
Let $A$ and $B$ be two events such that $P ( \overline { A \cup B } ) = \frac { 1 } { 6 } , P ( A \cap B ) = \frac { 1 } { 4 }$ and $P ( \bar { A } ) = \frac { 1 } { 4 }$, where $\bar { A }$ stands for the complement of the event $A$. Then the events $A$ and $B$ are
(1) Independent but not equally likely.
(2) Independent and equally likely.
(3) Mutually exclusive and independent.
(4) Equally likely but not independent.
Let $A$ and $B$ be two events such that $P ( \overline { A \cup B } ) = \frac { 1 } { 6 } , P ( A \cap B ) = \frac { 1 } { 4 }$ and $P ( \bar { A } ) = \frac { 1 } { 4 }$, where $\bar { A }$ stands for the complement of the event $A$. Then the events $A$ and $B$ are\\
(1) Independent but not equally likely.\\
(2) Independent and equally likely.\\
(3) Mutually exclusive and independent.\\
(4) Equally likely but not independent.