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Math Help - P[(a∩bc)u(ac∩b)]=p(a)+p(b) – 2p(a∩b).

  1. #1
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    Lightbulb P[(a∩bc)u(ac∩b)]=p(a)+p(b) – 2p(a∩b).

    show that :P[(A∩B^C)U(A^C∩B)]=P(A)+P(B) – 2P(A∩B).[/font]
    Last edited by compufatwa; October 30th 2007 at 07:40 AM.
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  2. #2
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    Recall that P(M) = P(MN) + P(MN^c ).
    \begin{array}{rcl}<br />
 P(AB^c  \cup A^c B) & = & P(AB^c ) + P(A^c B),\quad (AB^c  \cap A^c B = \emptyset ) \\ <br />
  & = & P(A) - P(AB) + P(B) - P(AB) \\ <br />
  & = & P(A) + P(B) - 2P(AB) \\ <br />
 \end{array}
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  3. #3
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    Lightbulb

    thanks alot plato
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