3.3.2 problem 39

Let $X$ have a discrete uniform distribution over values $1,2,3,...10$. Let $Y=11-X$. Then $Y$ is also discrete uniform over the same sample space, but $P(X=Y)=0$.

If $X$ and $Y$ are independent, then $P(X=Y)={\sum }_{i\in S}P(X=i)P(Y=i)>0$.