Let's say there are two machines, X and Y. X is connected to Y.
* If X is turned on, Y turns on 50% of the time.
* If Y turns on (through X being turned on) then it breaks 25% of the time.
* Y won't break spontaneously and it can only be turned on through X.
What is the joint probability distribution between Y turning on and Y breaking?
Considering the set of times that X turns on, what is the mutual information between Y turning on and Y breaking (how many bits)?
2. The attempt at a solution
I'm not really sure how to start or how to make the joint probability distribution.