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Probability Question

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Given that [tex]P[A|B]=P[A|B^c][/tex], prove that they are independent.

    3. 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.
  2. jcsd
  3. Sep 24, 2008 #2


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    Gold Member

    Try using the fact that [tex]
    P(A \cap \overline B ) = P(A) - P(A \cap B)[/tex], i think.
  4. Sep 24, 2008 #3
    Got it. This was unusually convoluted for something so trivial.
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