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What's the difference between P(A|B) and P(A|B=+ve) ? Are they the same or different ? Are the law of addition and multiplication applicable to both ?

Edit: Sorry, edited for clarity. I am talking about probability

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    @HenningMakholm .....and in the [Rao–Blackwell theorem](http://en.wikipedia.org/wiki/Rao-Blackwell_theorem).2011-10-27

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Maybe it's what are you looking for...

If $B=\{b_1,b_2\}$ or the event B have only two values and you call one of this, for example $b_1$ by True and the other, $b_2$, by False, so

$P(A|B)=P(A|B=True)$

because this is a convention for not always repeat $B=True$ every time you want to write it.

Example:

$Toothache=\{True,False\}$

$P(Caries|Toothache)=P(Caries|Toothache=True)$

by convention.