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Math Help - Need Help (axioms of probability)

  1. #1
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    Need Help (axioms of probability)

    I'm stuck on this last problem... I been rereading the textbook but can't figure where I went wrong ... Help please...

    At first, I thought it would only be A and subsets wouldn't apply to it. However, that was wrong :/.

    Q. Suppose 0<P(A)<1 and 0<P(B)<1. If A implies not B then (select all that apply)
    A. http://i47.tinypic.com/2v3o2rn.png

    Thank you so much.
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  2. #2
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    Re: Need Help (axioms of probability)

    Are you asking why H and I are true? Draw two non-overlapping circles A and B. Is it true that A is located inside the exterior of B?
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  3. #3
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    Re: Need Help (axioms of probability)

    It''s more like how I should approach this problem. I'm really confused... I understand when it is A implies B, but the "not B" is throwing me off...
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  4. #4
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    Re: Need Help (axioms of probability)

    Mathematics uses logical laws to build its arguments, and logical laws in turn are just a refinement of common sense. There are two ways to explain a basic logical argument. One is to posit axioms and rules of inference and to show how the argument conforms to them. This way is suitable to convince a computer, but it does not give much clarity to people. The other way is to see how the argument follows the same reasoning we use every day in ordinary life.

    Suppose A is the property of being a cat (which can be associated with the set of all cats), and B is the property of being a dog (or, again, the set of all dogs). Then A implies not B. Also, cats form a subset of all non-dogs and dogs form a subset of all non-cats.

    Note that the following statements are equivalent:

    (1) A and B are disjoint
    (2) A is a subset of the complement of B (or, A implies not B)
    (3) B is a subset of the complement of A (or, B implies not A)
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  5. #5
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    Re: Need Help (axioms of probability)

    Wouldn't my answers be right then? The generator has rejected the answer. I only have one submission left .
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  6. #6
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    Re: Need Help (axioms of probability)

    Quote Originally Posted by PennCow View Post
    Wouldn't my answers be right then?
    If A precludes B, would you say that A and B are independent?
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  7. #7
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    Re: Need Help (axioms of probability)

    Ok I get where you were going... I stuck with mutual exclusive since a friend of mine who I talked with was sure it was mutual exclusive... ... I still have trouble finding the difference b/w ME and independent...

    After some reading, it seems like they're dependent... umm...
    Last edited by PennCow; July 17th 2012 at 12:43 PM.
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  8. #8
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    Re: Need Help (axioms of probability)

    Quote Originally Posted by PennCow View Post
    I still have trouble finding the difference b/w ME and independent...
    Events A and B are independent if the fact that A occurred carries no information whether B occurred at the same time. For example, when you roll two dies, the result of the first roll says nothing about the result of the second one. Events A and B are mutually exclusive if the fact that A occurred carries a lot of information about B, namely, that B did not occur. For example, the event that a die roll produced 1 and the event that the same die roll produced 6 are mutually exclusive. Note, however, that mutually exclusive events are not necessarily exhaustive (the die roll could also produce 2, 3, 4 and 5).
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  9. #9
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    Re: Need Help (axioms of probability)

    Could it be that this could be both mutually exclusive and dependent then? Since A implies not B (mutual exclusive). Since B is somewhat relying on A, it'd be dependent? Would it just be:

    A: A and B are mutually exclusive ###
    B: A and B are independent
    C: A and B are dependent ###
    D: A is a subset of B
    E: B is a subset of A
    F: not A is a subset of B
    G: not B is a subset of A
    H: A is a subset of not B ###
    I: B is a subset of not A ###
    J: not B is a subset of not A
    K: not A is a subset of not B
    L: none of the above
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  10. #10
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    Re: Need Help (axioms of probability)

    Quote Originally Posted by PennCow View Post
    Could it be that this could be both mutually exclusive and dependent then? Since A implies not B (mutual exclusive). Since B is somewhat relying on A, it'd be dependent?
    Yes, since A gives full information about B (that B did not occur), A and B cannot be independent.
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  11. #11
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    Re: Need Help (axioms of probability)

    Can you double check my list of answer again one last time emakarov? I'm down to my last assignment submission and I just need this problem to get 100% on this homework . I don't want to screw up. It has been driving me crazy last night and so far today... Thanks a lot.

    A: A and B are mutually exclusive ###
    B: A and B are independent
    C: A and B are dependent ###
    D: A is a subset of B
    E: B is a subset of A
    F: not A is a subset of B
    G: not B is a subset of A
    H: A is a subset of not B ###
    I: B is a subset of not A ###
    J: not B is a subset of not A
    K: not A is a subset of not B
    L: none of the above
    Last edited by PennCow; July 17th 2012 at 01:10 PM.
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  12. #12
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    Re: Need Help (axioms of probability)

    This looks fine to me.
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  13. #13
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    Re: Need Help (axioms of probability)

    Thank you so much. Got 100% !
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