Given a randomised algorithm for a problem, is there a corresponding deterministic algorithm?
If the running time of the algorithm is bounded, in the sense that for every input $x$ there is a number $T(x)$ such that whatever the coin tosses are, the algorithm always terminates within $T(x)$ steps, then you can always "try all possibilities" and convert your randomized algorithm to a deterministic one, albeit with a possibly much larger running time.

For polynomial time algorithms in particular, it is conjectured that you can derandomize any algorithm with at most a polynomial blow-up in time, a conjecture usually stated as $\mathsf{P}=\mathsf{BPP}$.