Independent Events: Pr(A$\cap$B) = Pr(A)Pr(B)

[sara_87]

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]

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]

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!