Results 1 to 8 of 8
Like Tree3Thanks
  • 1 Post By abender
  • 1 Post By Plato
  • 1 Post By abender

Math Help - Conditional Probability

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Germany
    Posts
    8

    Conditional Probability

    Hi,

    I have a question concerning conditional probabilities. Suppose that P(a, b, c) is a discrete joint distribution. My problem is to express the conditional P(a, c | b) in terms of the conditional P(a | b, c).

    My approach:

    P(a, c| b) = P(a|b, c) P(c|b)

    Is this correct?

    Thanks and best wishes,

    samosa
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37

    Re: Conditional Probability

    Bayes' Theorem.

    P(A_i|A) = \dfrac{P(A_i) P(A|A_i)}{\sum^N_{j=1}P(A_j) P(A|A_j)}
    Last edited by abender; November 13th 2012 at 06:59 AM.
    Thanks from samosa
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Germany
    Posts
    8

    Re: Conditional Probability

    Hi,

    thanks for your help.But I do not find the desired relationship.

    Variant I: Bayes Theorem gives

    P(a | b, c) = P(b, c | a)P(a)/P(b,c)

    How do I get P(a,c | b) into the right hand side?

    Variant II: Bayes Theorem gives
    P(a, c | b) = P(b|a, c) P(a, c)/P(b)

    How do I get P(a | b, c) into the right hand side?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Conditional Probability

    Quote Originally Posted by samosa View Post
    Variant I: Bayes Theorem gives
    P(a | b, c) = P(b, c | a)P(a)/P(b,c)
    How do I get P(a,c | b) into the right hand side?


    In your class and/or textbook how are the symbols P(a,b|c)~\&~P(a|b,c) defined?
    Thanks from samosa
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37

    Re: Conditional Probability

    Quote Originally Posted by samosa View Post
    Hi,

    thanks for your help.But I do not find the desired relationship.

    Variant I: Bayes Theorem gives

    P(a | b, c) = P(b, c | a)P(a)/P(b,c)

    How do I get P(a,c | b) into the right hand side?

    Variant II: Bayes Theorem gives
    P(a, c | b) = P(b|a, c) P(a, c)/P(b)

    How do I get P(a | b, c) into the right hand side?

    P(X|Y) = \dfrac{P(X\cap Y)}{P(Y)}

    P(A\cap C|B)= \dfrac{\color{red}P(A\cap B\cap C)}{P(B)}

    P(A | B\cap C)= \dfrac{P(A\cap B\cap C)}{P(B\cap C)} \implies  P(A\cap B\cap C) = \color{red}P(A | B\cap C) P(B\cap C)

    P(A\cap C|B)= \dfrac{\color{red}P(A | B\cap C) P(B\cap C)}{P(B)}
    Thanks from samosa
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2012
    From
    Germany
    Posts
    8

    Re: Conditional Probability

    Hi Plato,

    perhaps this way:

    P(a,b|c) = P(a, b, c)/P(c)

    and

    P(a|b,c) = P(a, b, c)/P(b,c)

    Then we have

    P(a|b,c)P(b,c) = P(a,b|c)P(c)

    giving

    P(a|b,c) = P(a,b|c)P(c)/P(b,c)

    Is this correct?
    Last edited by samosa; November 13th 2012 at 07:07 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2012
    From
    Germany
    Posts
    8

    Re: Conditional Probability

    @abender, thanks a lot. Now I got it.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37

    Re: Conditional Probability

    Quote Originally Posted by samosa View Post
    @abender, thanks a lot. Now I got it.
    Your welcome -- good luck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 22nd 2011, 01:39 AM
  2. Conditional Probability using the Law of Total Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2010, 03:01 AM
  3. conditional probability
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: August 12th 2010, 02:38 PM
  4. Conditional probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 8th 2010, 04:37 AM
  5. Continuous probability - conditional probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 1st 2009, 01:21 AM

Search Tags


/mathhelpforum @mathhelpforum