Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $C$

share|cite|improve this question
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
up vote 2 down vote accepted

It is the second. ${}{}{}{}{}{}$

$\Pr(A|B,C)$ is an abbreviation for $\Pr(A|(B\cap C))$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.