We prove the first time-space lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai [Ajt99a, Ajt99b] in his time-space tradeoffs for deterministic RAM algorithms computing element distinctness and for Boolean branching programs computing a natural quadratic form. Ajtai's bounds were of the following form...