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Proving two events are independent given that one has a probability of 1

  1. Sep 20, 2011 #1
    Show that an event A is independent of every event B if P(A)=0 or P(A)=1.

    **I was able to prove the first part of this problem that is that the events are independent when P(A)=0. However I am stuck on the part where P(A)=1.

    I have this so far:

    P(A n B) = P(A)P(B/A)
    = (1)P(B/A)
    = P(B/A)

    If the events are independent then P(A n B) = P(A)P(B) = (PB)

    So basically i have to show P(B/A) = P(B)....but I do cannot find a way to do this.
  2. jcsd
  3. Sep 20, 2011 #2


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    Try it the other way:
    P(A n B) = P(B)P(A/B)
  4. Sep 20, 2011 #3
    Ok, so i started using that suggestion and got the following.....

    P( A n B) = P(B)P(A/B)
    then I was going to say that P(A n B) = P(B), but I how can I prove that P(A/B)=1 without assuming that A and B are independent.
  5. Sep 20, 2011 #4
    thanks for the suggestion, but I was able to solve this problem by using the complement.
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