Ok I'll have a crack at it, it might be wrong though
Let random numbers . It doesn't matter how many trials there are, but as long as the difference between the number of times a success (x) is flipped and a failure (y) is flipped is the same, then we will have increased by x-y = n-d to reach n.
Then there are ways to arrange the probabilities
Of course it requires to know 3 things:
3. The number of trials.
It also looks quite similar to hypergeometric distribution
thanks for posting this problem :P