By definition of conditional probability,
\(\mathbb P(X|Y)=\dfrac{\mathbb P(X\cap Y)}{\mathbb P(Y)}\)
If \(X\) and \(Y\) are independent, then \(\mathbb P(X\cap Y)=\mathbb P(X)\times\mathbb P(Y)\), which reduces the above probability to
\(\mathbb P(X|Y)=\dfrac{\mathbb P(X\cap Y)}{\mathbb P(Y)}=\dfrac{\mathbb P(X)\times\mathbb P(Y)}{\mathbb P(Y)}=\mathbb P(X)\)
This means the answer is the second choice.
