Find the joint distribution with 2 discrete random variables

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How do you find the following joint distribution P(X=r, Y=k)? So far I have gotten:

P(X=0, Y=0) = (0.4)(0.8) = 0.32

P(X=1, Y=1) = (1-0.4)(0.9) = 0.54

How do I go on to find P(X=0, Y=1)and P(X=1, Y=0)?

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Hint:

$P(X=0,Y=1)+P(X=0,Y=0)=P(X=0)$