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Homework Help: Probability - Independence Question

  1. Oct 1, 2006 #1
    I'm trying to get the idea of independent events well grounded in my mind, but I'm having some difficulty.

    First of all, what would a venn diagram for independent events look like? I know you have the two events intersecting, and the intersection is equal to the product of the probabilities of the two events.... But all I can picture is a normal diagram of two events intersecting, which by eyeballing looks just like the diagram of any 2 events (depndent or independent). Is there something unique to the diagram of independent events?

    Mathematically, I just need to know that [tex] P(A \cap B) = P(A)P(B)[/tex] . But I can't form a graphical intuition about this, which I think would help me a lot.

    Incidentally, I can't help but keep picturing the venn diagram of mutually exclusive events as a representation of independent events... But I know that is dead wrong, since mutually exclusive events are dependent.

    Can anyone help me clarify this in my mind? Thanks!!
     
  2. jcsd
  3. Oct 1, 2006 #2

    arildno

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    If B is independent of A, it means that the intersection of B with A is the SAME fraction of A's total area as the intersection of B with not-A is of not-A's area.
     
  4. Oct 1, 2006 #3
    I think I just got more confused. :smile:

    Isn't the intersection of B with not-A the same as not-A? giving the fraction to be simply 1?

    Obviously I must be missing something, big time.
     
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