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

Is there a formula for a conditional probability of many "conditions" I.e: $P(X|Y,Z,\ldots)$ That is how to compute $P(X)$ given $X,Y,\ldots$ Or given separately $P(X|Y)$ and $P(X|Z)$ is there a formula to compute $P(X|Y,Z)$

share|cite|improve this question

In principle, for two conditions, by the usual formula, we have $$\Pr(X|Y,Z)=\frac{\Pr(X\cap Y\cap Z)}{\Pr(Y\cap Z)}.$$ From simply knowing the conditional probabilities $\Pr(X|Y)$ and $\Pr(X|Z)$, and say $\Pr(Y)$ and $\Pr(Z)$, and even $\Pr(Y\cap Z)$, we cannot determine $\Pr(X|Y,Z)$.

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.