# Thread: Union of Conditional probability

1. ## 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

2. ## Re: Union of Conditional probability

Originally Posted by parklover
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
$\mathcal{P}[(B\setminus C)\cup (C\setminus B)]~?$

3. ## Re: Union of Conditional probability

Originally Posted by Plato
Could it possibly be
$\mathcal{P}[(B\setminus C)\cup (C\setminus B)]~?$
yes. you are right. aren't they the same thing?

4. ## Re: Union of Conditional probability

Originally Posted by parklover
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 $\mathcal{P}[(B\setminus C)\cup (C\setminus B)]=\mathcal{P}(B)+\mathcal{P}(C)-2\mathcal{P}(B\cap C)$.