Is it possible to calculate P(B) if one knows P(A,B,C), P(A,B), P(B,C), P(A), and P(C)?

  • $\begingroup$ If the events are independent, you certainly can. Doesn't seem possible to do in the general without some additional knowledge, e.g. if $ P(A \cup C) = 1 $, then Alex R's answer applies. You could also deduce the answer in general given some other knowledge of the conditional probabilities. $\endgroup$
    – gammer
    Commented Aug 2, 2016 at 0:34
  • $\begingroup$ You can even add P(A,C) to the list of probabilities given in the question - that still isn't enough information, in general, as can be seen fairly easily by experimenting with a Venn diagram. (I posted an answer illustrating this that assumed P(A,C) is given, because I misread the question as originally posted, then removed it after noticing my misread!) $\endgroup$
    – Silverfish
    Commented Aug 2, 2016 at 1:29


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.