If A and B are independent events of a random experiment such that $P(A \cap B)=\large\frac{1}{6}$ and $P(\bar A \cap \bar B)=\large\frac{1}{3},$ then $P(A)= $ (Here $\bar E$ is the complement of the event E)

Question

\[\begin {array} {1 1} (1)\;\frac{1}{4} & \quad (2)\;\frac{1}{3} \\ (3)\;\frac{1}{2} & \quad (4)\;\frac{2}{3} \end {array}\]