How is sampling random?

Lets talk in terms of sampling from a normal dist. Currently, I have understood 2 concepts:

  1. Sampling is done in such a way that the sampled points follow the same characteristics i.e the same mean and stdv as the distribution.
  2. The points having higher likelihoods are more likely to be sampled

Now if these conclusions are true, how is sampling random?

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It depends on what you mean by random.
There are a lot of different random distributions.

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One interpretation is that you don’t get the same value on each iteration and you can’t predict a priori which sample you will get on a particular iteration. All you can predict is that the samples will have the statistical properties specified.

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Points with higher likelihood (probability density) are indeed more likely to be sampled, but this doesn’t mean the process is deterministic. The likelihood function dictates the probability of observing different values, but the actual sample values are still random.

So lets take a example-
1-suppose we have a flight full of people,
the distribution of age of people inside a flight is lets say have the normal distribution with mean of 35 and deviation of 20.
2-Now look, we have the ability to select any person at random with equal probability right. (Hence the random sampling)
3-but the likelihood of that person turning out close to mean is more. that is of age close to 35.

This is how I have understood this, if I am wrong do let me know.

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