Simple joint probability distribution

[jetlam]

Homework Statement

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)?

Thanks.

2. The attempt at a solution

I'm not really sure how to start or how to make the joint probability distribution.

 

[EnumaElish]

http://en.wikipedia.org/wiki/Joint_probability_distribution

 

[jetlam]

http://en.wikipedia.org/wiki/Joint_probability_distribution

That isn't helpful... anyone else? Please? I can't figure it out.