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can you give an intuitive example of $X\bot (A\cap B)$ but not $X\bot A$ and not $X\bot B$ ?

Should be read as "X is unconditionally independent of $(A\cap B)$".

I'm looking for some real life example like the people getting home late in Could someone explain conditional independence?

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ihadanny
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    What does $\bot$ mean in the context of probabilities? – celtschk Apr 01 '17 at 05:40
  • So "unconditionally independent" just means "independent"? – bof Apr 01 '17 at 06:15
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    I don't know if this counts as a "real life" example but how about this: three balls are drawn, one by one without replacement, from an urn which initially contains two white balls and two black balls. The events are: A = "first ball is white", B = "second ball is black", X = "third ball is white". – bof Apr 01 '17 at 06:25

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