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Conditional probability

  1. Mar 31, 2010 #1
    Hallow! May any one please help me on conditional probability i actualy understand how it occurs but the formula? The logic behind it!

    ie P(A/B)=P(AnB)/P(B)
     
  2. jcsd
  3. Mar 31, 2010 #2
    Hey!

    you mean P(A|B) right? P(A/B) could be mistaken for P(A\B) ..the difference.

    Anyways, the concept behind this definition (debatably an axiom), is very simple.

    Imagine a Venn Diagram with A and B as two circles crossing each other giving rise to a shared mid-section.

    P(A) = [outcomes that give event A] divided by [the sample space [tex]\Omega[/tex]] (all possible outcomes)

    P(B) = [outcomes that give event B] divided by [the sample space [tex]\Omega[/tex]] (all possible outcomes)

    P(AnB) = [outcomes that are SHARED between A and B] divided by [the sample space [tex]\Omega[/tex]] (all possible outcomes)

    When they ask you for P(A|B), what they are asking you is:

    "what is the probability that A will happen given that we KNOW that B has happened". If we know that the circle B has been chosen the only part of A left that COULD happen is the intersection between A and B that they both share!

    Basically: P(A|B) = "what is the probability of A, considering that the ONLY available sample space is now B?"

    do you get it now? try and draw it out!
     
    Last edited: Mar 31, 2010
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