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The issue is determining the probability of the events in terms of $P(A)$, $P(B)$, $P(A∩B)$ given events $A, B$.

My question is regarding the difference b/w these two statements..

  • Either $A$ or $B$ or both.
  • At least one of $A$ or $B$.

Aren't they both $P(A∪B)$?

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You’re right: they are. –  Brian M. Scott Sep 5 '12 at 2:11
This seems more like logic. –  Pedro Tamaroff Sep 5 '12 at 2:14

2 Answers 2

up vote 2 down vote accepted

yes, they both represent the same event $A\cup B$

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99% of the time in probability, "or" means the (inclusive) union denoted by $\cup$. Sometimes an exclusive "or" is used, and it would be denoted by $\triangle$; this one is called the symmetric difference.

$$ A \triangle B = (A - B) \cup (B-A) $$

So an element is in the symmetric difference if its in one of the guys, but not both.

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