If \(P(A \cup B)=\frac{1}{2}, P(\bar{A}\cup \bar{B})=\frac{1}{2}\) and \(2P(A)=P(B)=P\) then \(p\) is equal to

\(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\) \(\frac{2}{3}\)

\(\frac{2}{3}\)

\(P(A\cap B)=1-P(\bar{A}\cup \bar{B})=\frac{1}{2},P(A\cup B)=P(A)+P(B)-P(A\cap B)\)