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
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
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.