One example uses with replacement and one example uses without replacement.
Marbles no replacement.
For example if we pick 2 marbles from a bag there are different possibilities of what we could do.
A visual tutorial on how to calculate probability with and without replacement using marbles.
If the population is very large this covariance is very close to zero.
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For example a marble may be taken from a bag with 20 marbles and then a second marble is taken without replacing the first marble.
As then name says it is a probability where something is not replaced.
This is called probability without replacement or dependent probability.
What is probability without replacement.
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When we sample without replacement and get a non zero covariance the covariance depends on the population size.
This video goes through 2 examples of probability.
Probability with replacement we take a marble put it back into the bag and pick another one.
The sample space for the second event is then 19 marbles instead of 20 marbles.
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In each we specify either replacement the marbles go back into the bag after each pull or no replacement.