Why is sampling without replacement acceptable with a large population?

When dealing with a larger sample space, such as population, and especially dealing with ratios, it is often better to leave it without replacement because the negligence of the difference is far too small to affect its overall probability.

Take 900 people as an example: 400 boys and 500 girls.

When selecting a girl and then another girl, we get the probability:

500/900 · 499/899

Notice the two probabilities as a separate unit and compare the two.

500/900 is 0.55555 ..., while 499/899 is 0.555061179 ...

The negligence of the two is far too small to affect its overall probability.

This is also important when ratios come into play with probability.

Thus, it is better to select people without replacement when there is a larger sample space.