The answer depends on various factors. Some of these are:
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The answer depends on how rare or common the selected trait is. For something that is very rare, you will need a much larger sample to get a reasonable estimate of proportion.
that you have a large variance in the population and/or your sample size is too small
A large trial is necessary to provide good sample that is representative of the population
First you have chose an estimator for what you want to know about the population. In general the level of variability in the result that any estimator provides will depend on the variability in the population. Therefore, the greater the variability in the population the larger your sample size must be. You will also need to decide how much precision is required in your estimate. The more precision you require the greater your sample size will have to be.
A sample is a subset of the population.