I was thinking, since $X, Y$ are from $N(0,1)$ and they are independent, then
$X - 2Y$ has a distribution of $N(0, 5)$. Then $X-2Y > 0$ has probability of $1/2$.
The above seems correct to me, though it seems like then $X>nY$ would have probability of $1/2$. That seems a bit wrong. Did I get anything wrong?