1. ## Stats problem

I was given a class problem,

Suppose we are interested in computing P(A, D), but we can only measure P(A|B, C, D).
Show how we can apply the Chain Rule and the Total Law to compute what we want.

At first thoughts i was thinking that since we are asked to use the total law events would all be pairwise mutually exclusive and thus P(A,D)=0. this may be naive thinking

I tried manipulating bayes theroem and got
P(A,D)=P(A/B,C,D)*P(B,C,D)/P(B,C/A,D)

Then i got stuck can anyone point me in the right direction?

2. ## Re: Stats problem

I'm guessing you have more information than that. You can't ONLY use P(A|B,C,D) to get what you want. What else do you know about these events?

3. ## Re: Stats problem

Suppose we are given P(C|D), P(A|B, C, D), and P(D). Use the Chain Rule to find what
missing conditional probability we need to measure in order to compute P(A, B, C, D).

It was a two part exercise this was part one if of any relevance,

the answer i got for the above was

P(B/C,D) is missing

as P(A,B,C,D)=P(A/B,C,D)*P(B/C,D)*P(C/D)*P(D)

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