Rewrite probabilities as boolean algebra

Posted by Magsol on Stack Overflow See other posts from Stack Overflow or by Magsol
Published on 2010-04-07T03:51:43Z Indexed on 2010/04/07 4:03 UTC
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Filed under:

math

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probability

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boolean-logic

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homework

I'm given three binary random variables: X, Y, and Z. I'm also given the following:

P(Z | X)

P(Z | Y)

P(X)

P(Y)

I'm then supposed to determine whether or not it is possible to find P(Z | Y, X). I've tried rewriting the solution in the form of Bayes' Theorem and have gotten nowhere. Given that these are boolean random variables, is it possible to rewrite the system in terms of boolean algebra? I understand that the conditionals can be mapped to boolean implications (x -> y, or !x + y), but I'm unsure how this would translate in terms of the overall problem I'm trying to solve.

(yes, this is a homework problem, but here I'm much more interested in how to formally solve this problem than what the solution is...I also figured this question would be entirely too simple for MathOverflow)

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