Let A be a randomized algorithm computing a function F with Prob(A(x) = F(x)) ≥ 1/3 for every argument x of F. Assume that one is aware of the fact that Prob(A(x) = α) ≤ 1/4 for every wrong result α (i.e., that the probability of computing any specific wrong result is at most 1/4). Can this knowledge be used to design a useful randomized algorithm for F?