Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$, $P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$, then which of the following is true?
- A$P(X \cap Y)=\frac{1}{5}$
- B$P(X \cup Y)=\frac{2}{5}$
- C$P(Y)=\frac{4}{15}$
- D$P(X \cup Y)=\frac{1}{2}$
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