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Consider two independent random variables $X$ and $Y$ with identical distributions. The variables $X$ and $Y$ take values $0,1$ and $2$ with probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ respectively. What is the conditional probability $P(X+Y=2 \mid X-Y=0) ?$

1. $0$
2. $\frac{1}{16}$
3. $\frac{1}{6}$
4. $1$