When 2 events have partial overlap isnt that always independent event since they have that small overlap that considers them both? If can, please my a example ive been trying to get out of this question for ages but cant imagine how
It looks like you’re assuming that any partial overlap (an intersection) automatically makes two events independent.
But I’m not sure why you would think that. How do you define the independence of two events?
I believe it’s because on gregmat, Ive only learned the 3 types of relationships: mutually exclusive, independent events, and the last one, one group inside another (I forget its former title). Are their other relationships I should know for the GRE?
Imagine two events A and B such that \mathbb{P}(A) = 0.4 and \mathbb{P}(B) = 0.3. Consider a Venn diagram of the two overlapping sets and visualize moving them closer together or farther apart, thereby varying the size of the overlapping region A \cap B. Hopefully, it should be clear that P(A \cap B) can take on any real value between 0 and 0.3 (inclusive).
Of the infinite set of possible values P(A \cap B) could assume, the only one that makes A and B independent is P(A \cap B) = 0.4 \cdot 0.3 = 0.12.
Consequently, one could argue that when the events are not mutually exclusive (having partial overlap), they are almost never independent. This is in stark contrast to what you initially inferred.
If you really want to classify the relationship between two or more events, you can just say they’re one of two things: independent or dependent.
I see,so independent events ONLY happen if the “both” is A times B if the both is bigger or smaller than the value of the product of A and B. It is NOT independent events?
Sure