This is an ill formed problem.

If all you need to do is pick one random number, just pick one: 0 or 1. That will be to any level of proof just as random as any natural method one could devise for a single number.

If instead the question is about generating a series of digits, and making an argument about the randomness of thosee digits, that is a completely different problem, and one that needs more specification about how much random data is needed and what context against which that randomness will be evaluated.