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Math Help - Union of Conditional probability

  1. #1
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    Union of Conditional probability

    P[(B /C) U (C / B)]

    what is the meaning of the expressions above?

    is it equal P(B /C) + P (C / B)- P(C joint B)
    and when P(C joint B)=0, P[(B /C) U (C / B)]=0
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  2. #2
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    Re: Union of Conditional probability

    Quote Originally Posted by parklover View Post
    P[(B /C) U (C / B)]

    what is the meaning of the expressions above?

    is it equal P(B /C) + P (C / B)- P(C joint B)
    and when P(C joint B)=0, P[(B /C) U (C / B)]=0
    Could it possibly be
    \mathcal{P}[(B\setminus C)\cup (C\setminus B)]~?
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  3. #3
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    Re: Union of Conditional probability

    Quote Originally Posted by Plato View Post
    Could it possibly be
    \mathcal{P}[(B\setminus C)\cup (C\setminus B)]~?
    yes. you are right. aren't they the same thing?
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  4. #4
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    Re: Union of Conditional probability

    Quote Originally Posted by parklover View Post
    yes. you are right. aren't they the same thing?
    Often B\setminus C is written B-C and it means B\cap \overline{C} where \overline{C} is C complement.

    So \mathcal{P}[(B\setminus C)\cup (C\setminus B)]=\mathcal{P}(B)+\mathcal{P}(C)-2\mathcal{P}(B\cap C).
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