Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let's two events $S1$ and $S2$ are conditionally independent given the event $A$, i.e.,

$P(S_1|S_2,A) = P(S_1|A)$ and $P(S_2|S_1,A) = P(S_2|A)$

If $B$ is an arbitrary event, does the following probability hold?

$P(S_1|S_2,A,B) = P(S_1|A,B)$?

share|improve this question
add comment

1 Answer

up vote 0 down vote accepted

No. We can ignore $A$-let it be certainly true. Let $S_1$ be a coin flip is heads and $S_2$ be a die roll is even. Now let $B$ be coin flip heads iff die roll is even. Then $P(S_1|S_2,B)=1, P(S_1|B)=\frac 12$

share|improve this answer
add comment

Your Answer

 
discard

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.