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Math Help - Conditional Probability problem

  1. #1
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    Conditional Probability problem

    Let S be a sample space, with A is a subset S and B is a subset S. If P(A) = .6 what can be said about, P(A ∩ B),
    when
    (a) A and B are mutully exclusive?
    (b) A is a subset B
    (c) B is a subset A
    (d) A′ is a subset B′
    (e) A is a subset B′

    Not entirely sure how to approach this problem...let me know if the first is on the right track.

    a) If A and B are mutually exclusive, P(A ∩ B)= P(A)P(B)
    Last edited by mike2208; September 19th 2011 at 12:03 PM.
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  2. #2
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    Re: Conditional Probability problem

    Quote Originally Posted by mike2208 View Post
    Let S be a sample space, with A is a subset S and B is a subset S. If P(A) = .6 what can be said about, P(A ∩ B),
    when
    (a) A and B are mutully exclusive?
    (b) A is a subset B
    (c) B is a subset A
    (d) A′ is a subset B′
    (e) A is a subset B′

    Not entirely sure how to approach this problem...let me know if the first is on the right track.

    a) If A and B are mutually exclusive, P(A ∩ B)= P(A)P(B)
    No, \mathcal{P}(A\cap B)=0.
    Mutually exclusive means A\cap B=\emptyset.

    Just as A\subseteq B means A\cap B= A
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  3. #3
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    Re: Conditional Probability problem

    That's right, if they are mutually exclusive then the probability they intersect is zero.

    So would B subset of A mean B ∩ A = B?
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  4. #4
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    Re: Conditional Probability problem

    Quote Originally Posted by mike2208 View Post
    That's right, if they are mutually exclusive then the probability they intersect is zero.
    So would B subset of A mean B ∩ A = B?
    Yes.

    One cannot do probability if one does not know all basic set operations.
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    Re: Conditional Probability problem

    Ok, I have all but the last.

    If A' is subset of B', then B is subset of A, so P(A ∩ B) = P(B).

    However, I still have not found any rules on the final question, A is subset of B'.
    Last edited by mike2208; September 19th 2011 at 02:07 PM.
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    Re: Conditional Probability problem

    Quote Originally Posted by mike2208 View Post
    I still have not found any rules on the final question, A is subset of B'.
    A \subseteq B'\; \iff \;A \cap B = \emptyset
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  7. #7
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    Re: Conditional Probability problem

    Oh thanks. I haven't seen that one before. I'm looking for the proof online. It's not listed in my textbook.

    I can see that easily from a diagram, but I'm trying to find a list of important set theory laws and indentities.
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  8. #8
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    Re: Conditional Probability problem

    Quote Originally Posted by mike2208 View Post
    Oh thanks. I haven't seen that one before. I'm looking for the proof online. It's not listed in my textbook.

    I can see that easily from a diagram, but I'm trying to find a list of important set theory laws and indentities.
    Think about it.
    A\subseteq B' says "all A's are not B's".
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