By your statement, there is no distribution restriction "if the number of samples taken is large enough." By placing all 10% of your '?' at the beginning and doing a tremendous number of samples, your "data full of ?" or "data of no ?" should even out to 10%. You just have to take a large number of samples.
Since neither the sample size, nor the number of samples is defined, it could just as easily be "one sample of ten percent plus one", the result of which would be that virtually every random solution would fail.
This looks like homework. The level of sophistication of your request changed dramatically from the original problem statement to the response you gave me.
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