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Calculating probability of an event

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the probability of the following statement :

    [tex]P(A\prime \cap C | B \prime )[/tex]



    2. The attempt at a solution

    [tex]P(A \prime \cap C | B\prime ) =\frac{P ( A \prime \cap C \cap B \prime)}{P(B \prime)}= \frac{P ( A \prime \cap C \cap B \prime)}{1-P(b)}[/tex]

    I am stuck as to how do l deal with the numerator. Can someone please help me ?
     
  2. jcsd
  3. Oct 15, 2009 #2

    lanedance

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    what are you trying to do?
     
  4. Oct 16, 2009 #3
    I am trying to calculate the probability of [tex]
    P(A\prime \cap C | B \prime )
    [/tex]. More of like trying to find the algebraic expression to calculate the probability of [tex]
    P(A\prime \cap C | B \prime )
    [/tex].
     
    Last edited: Oct 16, 2009
  5. Oct 16, 2009 #4

    lanedance

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    in terms of what? ie what form are you trying to simplify to/express in?
     
  6. Oct 16, 2009 #5
    I am trying to make it as simple as possible so that if given the values of A,B&C you can calculate the probability
     
  7. Oct 16, 2009 #6

    lanedance

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    sorry, its still not clear exactly what you;re trying to do, is this an actual question? given what values?

    you will need P(A), P(B), P(C) and some info about their intersections/unions

    you could use some basic set theory to re-arrange, but it all depends want you want it in terms of, for example, deriving quickly from venn diagrams

    looking at 2 sets A & B
    [tex] P(A) + P(B) = P(A \cup B) + P(A \cap B) [/tex]

    then adding another set C
    [tex] P(A) + P(B) + P(C) = P(A \cup B \cup C) + P(A \cap B) + P(B \cap C) + P(C \cap A) -P(A \cap B \capC) [/tex]
     
    Last edited: Oct 16, 2009
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