Correct answer = .13125
It looks like a super simple problem, but I am not sure what i'm doing wrong
My work: We want to calculate $P(X+Y =2)$, which divides into cases $P_{X,Y}(0, 2)+P_{X,Y}(1, 1)+P_{X,Y}(2, 0)$, each can be expressed as $\frac{P(Y=y|X=x)}{P(X=x)}$. Denominator we are given the expression. Numerator is simply the value in the table. What am I doing wrong?
You should go for: $$P\left(x+y=2\right)=P\left(x=0,y=2\right)+P\left(x=1,y=1\right)+P\left(x=2,y=0\right)=$$$$P\left(x=0\right)P\left(y=2\mid x=0\right)+P\left(x=1\right)P\left(y=1\mid x=1\right)+P\left(x=2\right)P\left(y=0\mid x=2\right)=$$$$0.5\times0.05+0.25\times0.3+0.125\times0.25=0.13125$$