Here's the question: Suppose that $X$ and $Y$ are uniformly distributed on the diamond $|x| + |y|<1$ Find $P(Y>1/4 | X=1/2)$.
My approach: 1) Draw the diamond. 2) Fix the line $x=1/2$ 3) Draw the line $y=1/4$ 4) Use double integral over the little triangle: $\int_{1/2}^{3/4}dx\int_{1/4}^{1-x} \frac{1}{2}dx$, where $\frac1{2}$ is the joint density of $X$ and $Y$, found by $\frac{1}{diamond \_ \ area}$ since we have a uniform distribution.
I just don't know why my approach gives me a wrong answer. It makes perfect sense to me. Please help. Thanks!