Suppose we are choosing a point inside the unit circle uniformly at random, that is the coordinate (X,Y ) of the point we choose is distributed with the joint probability density function $f_{x,y}(x,y)=\begin{cases}\frac{1}{\pi} & x^{2}+y^{2}\leq1\\0 &else\end{cases}$
find the probability $P(Y>0.5|\mid X\mid+\mid Y\mid<1)$ I know that it is a continuous probability so it need to integrate it i know that p(y>0.5) is equal to $\int_{0.5}^{1} \int_{-\sqrt{1+x^{2}}}^{\sqrt{1+x^{2}}} \frac{1}{\pi}dx dy$ but I got no idea with |x|+|y|<1