Let \(X\) and \(Y\) be two events such that \(P(X|\displaystyle Y)=\frac{1}{2},\ P(\displaystyle Y|X)=\frac{1}{3}\) and \(P(X\displaystyle \cap\ Y)=\frac{1}{6}\). Which of the following is (are) correct?
1
\(P(X\displaystyle \cup Y)=\frac{2}{3}\)
2
\(X\) and \(Y\) are independent
3
\(X\) and \(Y\) are not independent
4
\(P(X^{C}\displaystyle \cap Y)=\frac{1}{3}\)