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Given two events, A and B, if it is the case that "at least one of the events occurred", I have seen it written that we can identify that probability as $$pr(A \cup B)$$

I'm struggling to understand why a union symbol would represent the probability of at least one having occurred. Perhaps this is a silly misunderstanding, but wouldn't the union symbol represent them both having occurred?

Or is that: when we say "at least", we must consider the probability of one occurring, the other occurring, or both occurring, and so we ensure our safety by reaching for the least probably one, them both occurring, represents by the probability of the union of the two events?

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The event $A\cup B$ occurs if $A$ occurs, if $B$ occurs or if both $A$ and $B$ occur.

The event $A\cap B$ occurs if both $A$ and $B$ occur.

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  • $\begingroup$ oh, wow so the union is sort of like the "or" in logic, being true when either one occurs or both occur? $\endgroup$
    – compguy24
    Apr 24, 2014 at 8:34
  • $\begingroup$ @compguy24 Yes, you are precisely right. $\endgroup$
    – Cm7F7Bb
    Apr 24, 2014 at 8:35

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