According to the explanation, because there can be different types of overlap, a partial overlap “could be” independent events.
However, wouldn’t partial overlap include all of the different types of overlaps that the explanation mentions–whether the overlap is tiny or huge? And thus, wouldn’t having an overlap itself make the two events definitely independent?
Two events are independent iff \mathbb{P} (A \cap B) = \mathbb{P} (A) \cdot \mathbb{P} (B), so the overlap has this “constraint” in place.
I have the same question. can you please elaborate?
What do you need elaborated? The overlap should be exactly equal to the product of the individual probability (for 2 sets at least), as mentioned prior.
It isn’t otherwise and follows trivially from the definition itself.
