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Let \( X \) and \( Y \) be two events such that \( P(X \mid Y)=\frac{1}{2}, P(Y \mid X)=\frac{1}{3} \) and \( P(X \cap Y)=\frac{1}{6} \). Which of the following is (are) correct ?
\( \mathrm{P} \)
(A) \( P(X \cup Y)=\frac{2}{3} \)
(B) \( X \) and \( Y \) are independent
W
(C) \( X \) and \( Y \) are not independent
(D) \( P\left(X^{C} \cap Y\right)=\frac{1}{3} \)
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