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Number of elements for a given probability?

  1. Oct 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Let A be a set with 8 elements and B be a set such that A U B has 12 elements. What is the number of elements in P(B\A) U P(∅)?

    2. Relevant equations



    3. The attempt at a solution

    I have no idea what it means to ask what are the number of elements in a probability.. Is it the number of elements that would represent that probability?
     
    Last edited: Oct 30, 2012
  2. jcsd
  3. Oct 30, 2012 #2

    tiny-tim

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    Hi V0ODO0CH1LD! :smile:
    That P is (probably) the power set, the set of all subsets of the thing inside the brackets. :wink:

    (see http://en.wikipedia.org/wiki/Power_set)
     
  4. Oct 30, 2012 #3
    Okay, I red about power sets but I couldn't find anything on how to operate with them.

    Also, can I say that |A U B| = |A| + |B| - |A(intersect)B|?
    Because then I could say 12 = 8 + |B| - |A(intersect)B|
    Which would imply that 4 = |B| - |A(intersect)B| = |B\A|
    And that would mean that P(B\A) U P(∅) = 2^4 + 1 = 17

    Is that correct?
     
  5. Oct 30, 2012 #4

    tiny-tim

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    Yup! |(B\A)| = 4, so P(B\A) = 24, and P(∅) = 20 = 1 :smile:

    (but do they intersect? :wink:)
     
  6. Oct 30, 2012 #5
    Thanks a lot!! I would think they don't intersect because if |(B\A)| = 4 and |A U B| = 12 and |A| = 8 then that means |B| = 4.
     
  7. Oct 30, 2012 #6

    tiny-tim

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    No, i mean, do P(B\A) and P(∅) intersect? :wink:
     
  8. Oct 30, 2012 #7
    Ohh!! So the answer is actually 16??
     
  9. Oct 30, 2012 #8

    tiny-tim

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    Probably! :biggrin:
     
  10. Oct 30, 2012 #9
    Ha! Thanks!
     
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