Suppose I have two coins one is baised i.e its probality of head $\ne 0.5$ and another is a fair one with head and tails as equally likely outcome.
Now I begin tossing the baised coin first and note down the results for very large number of experiments(finite), then I switch to the fair one and do the some but this time I do it for even a larger number.
Then I note the total number of heads and total number of tails.
Now my question : If I perform the experiment with fair coin for a very large number would it be able to hide the fact that a unfair coin was involved?
Absolutely, but the ratio of fair coin flips to unfair coin flips (in order to hide that an unfair coin was ever used) is dependent on the unfairness of the biased coin.