Let $P$ be a probability measure over $\mathbb{R}$:
$$P((x,\infty)) = \begin{cases} \left(1+\frac{x}{2}\right)^{-2}, & x\gt0 \\ 1 , & \text{else} \end{cases}$$
Calculate $P((2,3])$.
I think I need to find a clever way to represent $(2,3]$ as union of open intervals but I'm not able to find a way to do so without getting an interval of the form $(-\infty,y)$.
Please any help or direction.
Hint:
$(2,3]\cup(3,\infty)=(2,\infty)$
The set on LHS are disjoint and a probability measure is additive.