Probability Question

  • Thread starter Dragonfall
  • Start date
  • #1
1,030
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Homework Statement


Given that [tex]P[A|B]=P[A|B^c][/tex], prove that they are independent.


The Attempt at a Solution



So we have that [tex]\frac{P(A\cap B)}{P(B)}=\frac{P(A\cap B^c)}{P(B^c)}[/tex]. I would have to show that [tex]\frac{P(A\cap B^c)}{P(B^c)}=P(A)[/tex]. I can't make that happen.
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
Try using the fact that [tex]
P(A \cap \overline B ) = P(A) - P(A \cap B)[/tex], i think.
 
  • #3
1,030
4
Got it. This was unusually convoluted for something so trivial.
 

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