I have some notes which introduces the quantifier $\exists^+x$ and interprets it as "the overwhelming majority of $x$". Then, it defines RP (Randomized Polynomial) as: $$ L\in RP\Leftrightarrow \exists R\in P: \begin{cases} x\in L \Rightarrow \exists^+y R(x,y)\\ x\notin L\Rightarrow \forall y\neg R(x,y) \end{cases}$$ If we consider the computation tree of the algorithm that recognizes $L$, we can interpret $x$ as the input of the algorithm and $y$ as the paths of the computation tree of the algorithm for input $x$. Then, $R(x,y)$ can be interpreted as "Path $y$ accepts for input $x$".
In these notes, it says that if an RP algorithm accepts, then we're sure the answer is correct, while rejection comes with an error. How come? This is confusing me because in the definition, error seems to be for inputs that are accepted. Could someone please explain to me? Is this correct?