Two Independent Random Variable

Question

To show that two random variable $X$ and $Y$ (for discrete case) are not independent, is it suffices to show that $P(X=x|Y=y)\neq P(X=x)$ for a certain $x$ and $y$? Or I should list out all the possible events and conclude $f(x,y)\neq f_1(x)f_2(y)$?

Answer 1

It is enough to find one pair $x,y$ with $P(X=x|Y=y) \neq P(X=x)$.

Answer 2

Both methods are valid, just choose the one which is done easier. But I’m not sure what you mean by list out all possible events”.