Finding sample size given confidence interval for an unknown distribution

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Is it possible to find sample size given confidence interval for an unknown distribution? If so, what parameters of the distribution are needed?

This came from the problem: There is a population of size 10^12, each individual has a value of either 0 or 1, we don't know what the distribution of the population is, and we want to estimate the percentage of 0 and 1 of the population. What should we do? How many samples do we need?

Edit: each individual does NOT take 0/1 with the same probability, so it's not Bernoulli distribution.