Summary: In this paper we introduce a new concept of probability (state) on \(n\)-nuanced MV-algebras and we prove some of its properties. As a main result, we prove that there is a one-to-one correspondence between the set of states on an \(n\)-nuanced MV-algebra \(L\) and the set of states of its MV-center \(M(L)\). We also introduce the notion of a conditional state on an \(n\)-nuanced MV-algebra \(L\) and we prove that the computation of a conditional state on \(L\) can be reduced to the computation of the state obtained by restriction to \(M(L)\). We define the notion of a continuous state on \(L\) based on the order convergence and we prove that any continuous state is a submeasure.