I have a question concerning conditional probabilities. Suppose that P(a, b, c) is a discrete joint distribution. My problem is to express the conditional P(a, c | b) in terms of the conditional P(a | b, c).
P(a, c| b) = P(a|b, c) P(c|b)
Is this correct?
Thanks and best wishes,
thanks for your help.But I do not find the desired relationship.
Variant I: Bayes Theorem gives
P(a | b, c) = P(b, c | a)P(a)/P(b,c)
How do I get P(a,c | b) into the right hand side?
Variant II: Bayes Theorem gives
P(a, c | b) = P(b|a, c) P(a, c)/P(b)
How do I get P(a | b, c) into the right hand side?