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Events (or random variables) are independent when information on some of them tells you nothing about the probability of occurrence (/ distribution) of the others. Please DO NOT use this tag for independent variable use [predictor] instead.
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Need intuition about independence of events
I believe the idea of independence is, using your Venn diagram, that the proportion of A in B is equal to the proportion of A in Ω. … Substituting P(A) for P(A|B), we get the formal definition of independence for two events: P(AB) = P(A)P(B) …