Circuit drawings probability

In each of the “circuit drawings” below, every one of the numbered switches will be closed (which allows current to flow) with probability p, independently of all other switches. In each drawing, find the probability that current can flow between A and B.

http://farm5.static.flickr.com/4147/...ca41def8b0.jpg

I'm not really sure where to begin with this. For (a), the current would flow with the anything except if only (1,2), (3,4), (1), (2), (3), (4), or (none) are closed. But where do I go from here?