Here are some examples from Moore (2007) that you might find helpful for understanding the differences between independent/dependent events.
If a nurse measures your height twice, it is reasonable to assume that the two results are independent observations. Each records your actual height plus a measurement error, and the size of the error in the first result does not influence the instrument that makes the second reading. But if you take an IQ or other mental evaluation twice in succession, the two test scores are not independent. The learning that occurs on the first attempt influences your second attempt.
What are some other examples?
Moore, D. (2007).The basic practice of statistics (4th ed). New York, NY: W. H. Freeman and Company.
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