Bayes Rule, Probability, determine whether dependant or independant

Question

I need to determine whether or not x and y are independent from each other, using the data supplied below. I think the solution should use bayes rule/product rule/some independence rule. I just can't see how to determine independence/dependence.

X=0
Y=0
P(X=0,Y=0) = 0.15

X=0
Y=1
P(X=0,Y=1) = 0.20

X=1
Y=0
P(X=1,Y=0) = 0.35

X=1
Y=1
P(X=1,Y=1) = 0.30

Answer 1

Hint: It is enough to check whether or not $$P(X=1,Y=1) = P(X=1)P(Y=1) \\= [P(X=1,Y=0)+P(X=1,Y=1)]\times [P(X=1,Y=1)+P(X=0,Y=1)]$$