Darts on a ruler probability If two points are selected at random on an interval from 0 to 1.5 inches, what is
the probability that the distance between them is less than or equal to 1/4"?

The square $S=\{(x,y) | x,y \in [0, \frac{3}{2}] \}$ has area $(\frac{3}{2})^2$. The area $\Delta= \{(x,y) \in S \, |\,  |x-y| > \frac{1}{4} \}$ can be easily rearranged to be a square with area $(\frac{3}{2}-\frac{1}{4})^2$. Hence the chance of landing in $S \setminus  \Delta$ is $\frac{(\frac{3}{2})^2-(\frac{3}{2}-\frac{1}{4})^2}{(\frac{3}{2})^2} = 1 - (1-\frac{1}{6})^2 = \frac{11}{36}$.
