Arrow and turnstile interpolations are investigated in UCL (introduced in [SRSM13]), a logic that is  a complete extension of classical propositional logic for reasoning about  connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos. The talk reports on joint work with Amílcar Sernadas and Cristina Sernadas.