# Union of Conditional probability

• Aug 16th 2011, 12:53 PM
parklover
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
• Aug 16th 2011, 12:56 PM
Plato
Re: Union of Conditional probability
Quote:

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
$\mathcal{P}[(B\setminus C)\cup (C\setminus B)]~?$
• Aug 16th 2011, 01:14 PM
parklover
Re: Union of Conditional probability
Quote:

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?
• Aug 16th 2011, 01:25 PM
Plato
Re: Union of Conditional probability
Quote:

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