An event happens in a given hour with probability $p$. In advance, somebody predicts the event (successfully) with probability $p_1$ when it does occur and (incorrectly) predicts it with probability $p_0$ when it does not occur. Given this person predicts the event in the next hour, what's the probability that it will actually happen?
Is this a place where one should use the law of total probability? So, $p_1p + p_0(1-p)$?