I was trying to think of a scenario where we draw two random samples from two different populations. Can it be a case that the samples are independent but the populations are not?

EDIT: By independent sampling, I mean that if I draw 1st sample with some observations, and then I draw a 2nd sample such that the probability of occurrences of observations in this sample is independent of the observations I got in the 1st sample. My question is, can this happen even if the populations of the two samples are dependent (let's say as an extreme case, if the populations are same)?

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    $\begingroup$ What does it mean for two samples to be independent? What you've written is quite vague...can you try to sharpen your question? $\endgroup$ – lulu Feb 23 at 17:23
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    $\begingroup$ You might be confusing the linguistic or colloquial meaning of the word "independent" with the mathematical meaning of the word "independent." You might also be confusing the word "disjoint" or "exclusive" here as well. $\endgroup$ – JMoravitz Feb 23 at 17:25
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    $\begingroup$ Now... when we talk about independence in probability, we are referring specifically to events being independent or not... not outcomes. We can indeed draw multiple times without replacement and have the events described be independent. For instance, if you draw two cards from a standard deck of cards without replacement, the event that the first card is a king is independent of the event that the second card is a heart. This, even despite it being the same deck that both cards were drawn from. It didn't need to be two different distinct decks for it to be independent. $\endgroup$ – JMoravitz Feb 23 at 17:28
  • $\begingroup$ @JMoravitz I have edited my question. Maybe have a look at it now? $\endgroup$ – Avneesh Khanna Feb 24 at 8:53
  • $\begingroup$ What do you mean with a population? $\endgroup$ – user Feb 24 at 8:58

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