Join Probability & Random Variables

Hello, I'm very confused how to solve this problem... since I'm very low at math maybe someone can help me.

Assume a black bag containing 5 BLUE balls 3 RED balls and 2 GREEN balls. if we drew 2 balls arbitrarily from this black bag, using X to represent the number of BLUE balls drawn, and Y to represent the number of RED balls drawn, compute the following items :

a. the joint probability function f(x,y);

b. P[(X,Y) E A], where A is the region {(x,y)|x+y<=1}

c.When Y=1, find f(x|y=1) (i.e the conditional distribution for X, when Y=1), then using it to determine P(X=0|Y=1);

d.Prove this two random variables X and Y are not statistically independent

I've try to answer the point a

P(x,y) = P(x).P(x|x)+ P(x).P(y|x)+ P(y).P(y|y)+ P(y).P(x|y)

but I'm not sure whether it's correct or not...

Thanks in advance