Consider twoindependentrandom variables: $\displaystyle r,s$, where

$\displaystyle r\sim f(r)$ and $\displaystyle s \sim U[0,x]$.

($\displaystyle U[0,x]$ means uniform within support $\displaystyle 0$ and $\displaystyle x$.)

What is the following probability:

$\displaystyle \Pr (r-ts>p)$, where $\displaystyle t$ and $\displaystyle p$ are constants.

Any suggestions, tips or ideas?