NIMCET 2024 Paper

We know that ${\mathit{x}}^2+{\mathit{y}}^2=4$ is a circle and its one fourth part lies in the first quadrant. In the point $\mathit{P}=\left(\mathit{r},\mathit{s}\right),\mathit{r}$ and $\mathit{s}$ are $\mathit{x}$ and $\mathit{y}$ coordinates, and we need to find the probability that $\mathit{x}>\mathit{y}$. The shaded part is the favourable area and the area of the circle in the first quadrant is the sample space.
Hence the required probability $=\frac{1}{2}$