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Conditional probability question with set theory things

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Basically, I'm given the probability of 4 independent events:

    P(A) = 0.04
    P(B) = 0.03
    P(C) = 0.02
    P(D) = 0.01

    If any one of these occur, a failure will happen.
    More than one can happen at the same time.

    I need to find the probability that more than one of them has occurred given at least one as occurred.

    2. Relevant equations



    3. The attempt at a solution

    I solved for the prob that at least one occurred:
    Let F = A∪B∪C∪D
    Then P(F) = P(A) + P(B) + P(C) + P(D) - P(A∩B∩C∩D) = 0.09999976

    Now I have to solve for prob of 'more than one' occurred given F has occurred.
    I'm stuck on this part.
    How do I represent 'more than one occurred' with symbols?
    Would it be E = (A∩B)∪(A∩C)∪(B∩D)∪(C∩D)?

    Then P(E | F) ?
     
  2. jcsd
  3. Sep 29, 2011 #2
    No one..?
    Is my post not understandable?
     
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