Let \( \mathrm{X} \) and \( \mathrm{Y} \) be two events such that \( \mathrm{P}(\mathrm{X} \mid ...

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