Statement
The result is that two independent events become conditionally dependent (negatively dependent) given that at least one of them occurs. Symbolically:
- if 0 < P(A) < 1 and 0 < P(B) < 1,
- and P(A|B) = P(A), i.e. they are independent,
- then P(A|B,C) < P(A|C) where C = A∪B (i.e. A or B).
In words, given two independent events, if you only consider outcomes where at least one occurs, then they become negatively dependent.
Read more about this topic: Berkson's Paradox
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