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Math Help - Probabiltiy:

  1. #1
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    Probabiltiy:

    Given P(A) = .4, P(B) = .5, and P(A or B) = .7,
    a)find P(A and B)

    b)find P(A/B)

    c)find P(B/A)

    d)are A and B independent? Why, or why not?


    Had trouble with this of probability question on my exam..any help is much appreciated...Thanks!
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  2. #2
    Member Focus's Avatar
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    a) \mathbb{P}(A \cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)
    b),c) \mathbb{P}(A|B)=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}
    d) Independence (probability theory) - Wikipedia, the free encyclopedia
    Last edited by mr fantastic; November 23rd 2009 at 01:05 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lisa1984wilson View Post
    Given P(A) = .4, P(B) = .5, and P(A or B) = .7,
    a)find P(A and B)

    b)find P(A/B)

    c)find P(B/A)

    d)are A and B independent? Why, or why not?


    Had trouble with this of probability question on my exam..any help is much appreciated...Thanks!
    Draw a Venn diagram, and use it to determine P(A and B) (that is A intersection B)

    That should allow you to answer a), b) and c). For d) you need to determine if:

    P(A and B)=P(A)P(B)

    (when A and B will be independednt and not if this does not hold) and you have sufficient data to do so.

    CB
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Focus View Post
    I don't believe this is a university question but here are some hints;

    a) \mathbb{P}(A \cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)
    b),c) \mathbb{P}(A|B)=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}
    d) Independence (probability theory) - Wikipedia, the free encyclopedia

    from that link....
    Two events A and B are independent if and only if Pr(AB) = Pr(A)Pr(B).
    Last edited by matheagle; November 22nd 2009 at 08:58 PM.
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  5. #5
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    Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

    a)find P(A and B) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2

    b)find P(A/B) P(A/B)=P(A or B)/P(B)=.7/.5=1.4

    c)find P(B/A) P(B/A)=P(A or B)/P(A)=.7/.4=1.75

    d)are A and B independent? Why, or why not?

    Not independent because P(A or B) does not equal P(A)P(B)
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

    a)find P(A and B) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2

    b)find P(A/B) P(A/B)=P(A or B)/P(B)=.7/.5=1.4

    c)find P(B/A) P(B/A)=P(A or B)/P(A)=.7/.4=1.75

    d)are A and B independent? Why, or why not?

    Not independent because P(A or B) does not equal P(A)P(B)
    OR is union while AND is intersection.
    you need AND
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  7. #7
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    I'm sorry...I'm just having trouble with this one, I did get this wrong on my exam. I'm just trying to get it right so can practice it before my next exam.
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  8. #8
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    Given P(A) = .4, P(B) = .5, and P(A or B) = .7,

    a) P(A and B)=P(A)+P(B)-P(A or B)=.4+.5-.7=.2 YES

    b) P(A/B)=P(A or B)/P(B)=.7/.5=1.4>1 means this is WRONG

    c) P(B/A)=P(A or B)/P(A)=.7/.4=1.75> 1 means this is WRONG

    d)are A and B independent? Why, or why not?

    Not independent because P(A or B) does not equal P(A)P(B)
    b) P(A/B)=P(A AND B)/P(B)=.2/.5=.4
    c) P(B/A)=P(A AND B)/P(A)=.2/.4=.5

    They are indeed independent since P(A|B)=P(A) which holds whenever P(AB)=P(A)P(B) same with P(B|A)=P(B)
    as I said yesterday.
    Last edited by matheagle; November 22nd 2009 at 08:58 PM.
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