anonymous
  • anonymous
how are disjoint and independent different
Mathematics
jamiebookeater
  • jamiebookeater
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Zarkon
  • Zarkon
Two events A and B are disjoint if \(A\cap B=\emptyset\) A and B are independent if \(P(A\cap B)=P(A)\times P(B)\)
anonymous
  • anonymous
thanks
anonymous
  • anonymous
so if A and B were disjoint P(A U B)= P(A)+P(B) ?

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Zarkon
  • Zarkon
another way to look at it if A and B are disjoint...then if I know event A occurs then that means that B cannot occur..thus A and B are dependent (provided their individual probabilities are nonzero)
Zarkon
  • Zarkon
yes
anonymous
  • anonymous
I will remember that" when it is disjoint it is not independet"
Zarkon
  • Zarkon
correct...provided the nonzero probabilities
anonymous
  • anonymous
ok
Zarkon
  • Zarkon
since if P(A)=0 then \(P(A\cap B)=0\) and thus \[0=P(A\cap B)=P(A)\times P(B)=0\times P(B)=0\]

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