The bigger the sample size the more accurate the results will be.
For example, if you roll a 6 sided die and track the results to get the probability of rolling a six. If you only roll 6 times, then you may not even get one 6 or you could get a few. A small sample size means you won't get very reliable results.
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In a probability sample, each unit has the same probability of being included in the sample. Equivalently, given a sample size, each sample of that size from the population has the same probability of being selected. This is not true for non-probability sampling.
Factors that determine sample size
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In the context of a sample of size n out of a population of N, any sample of size n has the same probability of being selected. This is equivalent to the statement that any member of the population has the same probability of being included in the sample.
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