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Probability proof - what formulas are needed here?

  1. Apr 27, 2008 #1
    If events A and B are in the same sample space:
    • .
    Proove that if P(A I B') > P(A) then P(B I A) < P(B)

    (where B' is the Probability of A given not B)


    • .
    Proove that if P(A I B) = P(A) then P(B I A) = P(B)

    do we assume independence here so that P(A I B) = [P(A)*P(B)]/ P(B) = P(A) and state that since P(A n B) = P(B n A) that P(B I A) = [P(B)*P(A)] / P(A) = P(B) or is it wrong to assume independence here?
     
  2. jcsd
  3. Apr 27, 2008 #2

    exk

    User Avatar

    For the second proof use the fact that P(A|B)=P(A&B)/P(B) and similarly for the other one. You can't assume independence, but it is easy to see that they are using the usual definition of independence P(A&B)=P(A)P(B).
     
  4. Apr 27, 2008 #3
    Please could you show me the steps you would take
     
  5. Apr 30, 2008 #4
    assume
    [tex]P(A|B')>P(A)[/tex]
    then

    [tex]\frac{P(A\cap B')}{P(B')}>P(A)[/tex]

    [tex]\frac{P(B'|A)P(A)}{P(B')}>P(A)[/tex]

    [tex]\frac{P(B'|A)}{P(B')}>1[/tex]

    [tex]P(B'|A)>P(B')[/tex]

    [tex]1-P(B'|A)<1-P(B')[/tex]

    [tex]P(B|A)<P(B)[/tex]

    the other one isn't much different
     
  6. May 1, 2008 #5
    Thanks soo much!!
     
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