## What is the distribution of the following event?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

 Recognitions: Homework Help For any $a, b, c \in \{-1,1\}$ we have $$P(x=a|y=b,z=c) = \frac{P(x=a \cap \{y=b,z=c\})}{P(y=b,z=c)} = \frac{P(x=a,y=b,z=c)}{P(y=b,z=c)},$$ where $P(y=b,z=c) = \sum_{w=-1}^1 P(x=w,y=b,z=c).$ This has nothing to do with Physics or the Ising model or anything else like that; it is just elementary probability. RGV