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Independent Events

  • Thread starter sara_87
  • Start date
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My teacher gave these notes:

In general, if any two events A and B we find that Pr(B|A)=Pr(B), or equivantly,
Pr(AnB)=Pr(A)Pr(B),

then the events A and B are independent.



but i thought that when A and B are independent then Pr(AnB)=0?
what is my teacher trying to say, have i misunderstood something?
(btw n represents intersection)
 

Hurkyl

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P(A intersect B) = 0 means they're disjoint. Disjoint events are almost never independent. (If you have knowledge that A happened, you're certain that B didn't happen, so the two events cannot be independent)
 

HallsofIvy

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P(A and B)= P(A) P(B) means they are "independent". P(A and B)= 0 means they are "mutually exclusive": it one happens, the other can't. That's certainly not independent!
 

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