I have a signal gathering system. Every 10 seconds it goes to locations A, B and C and sees whether there is activity or not. It then populates a table which looks like following:
A B C ------------ 1 0 1 1 1 0 1 0 1 1 0 1 ............
There are about 10,000 such rows of data in table.
Now I want to understand $P(B,C|A)$.
My understanding is that I would have 8 cases here like the following: $P(B=1,C=1|A=1)$, $P(B=1,C=1|A=0)$, $P(B=1,C=0|A=1)$, etc.
My questions are :
Should I model this as binomial distribution or Dirichlet distribution. Why choose one over the other for this case?
I know that the way logic has been coded, B and C are impacted by activity at A. But what if C is also impacted by activity at B. Does considering binomial or Dirichlet distribution factor any interaction between B and C in calculating $P(B=1,C=0|A=1)$ for example?
I am pretty much of novice in this field so please explain your answer.
This question came out of the discussion on this previous question: Creating conditional probability distribution