# Conditional probabilities and order of operation

I see terms of the form $P(A|B,C)$ a fair bit. Which of the following is true?

1. $P(A|B,C)$ is the joint probability of $A|B$ and $C$

2. $P(A|B,C)$ is the probability of $A$ given both $B$ and $C$

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The second reading would make little sense as "given $B$" would necessarily apply to both $A$ and $C$. i.e. this would rather produce $P((A\cap C)|B)$. –  Hagen von Eitzen Nov 27 '12 at 23:32
The first reading you mean? Yes, I see - thanks. –  oadams Nov 27 '12 at 23:38

It is the second. ${}{}{}{}{}{}$
$\Pr(A|B,C)$ is an abbreviation for $\Pr(A|(B\cap C))$.