Let A and B be two events such that $P( \bar {P \cup B})=\large\frac{1}{6}$, $P(A \cap B)=\large\frac{1}{4}$ and $P(\bar {A})=\large\frac{1}{4}$, where $\bar {A}$ stands for the complement of the event A. Then the events A and B are :

Question

$\begin{array}{1 1}(A)\;\text{mutally exclusive and independent}\\(B)\;\text{equally likely but not independent}\\(C)\;\text{independent but not equally likely}\\(D)\;\text{independent and equally likely}\end{array} $