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When is it safe to use the binomial probability if the random selection does NOT use replacement? 'Define any variables you use'. I can think of a factory-line example where the sample space is constantly regenerating, I'm not sure how to put that in terms of 'variables' though.
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Or perhaps there's a theory on if the sample space is really big, then using the binomial without replacement is still a good approximation. (Source: Wikipedia).
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