Maybe I'm misreading his intent:
Are those binomials just for no searches done?
If so, how does finding a site with a search affect things?
Edit: Ok, you posted while I was typing. Thanks. I was thinking of them independently. And I still think that may be possible.
I'd love to see a table without the probabilities for the different paths/terrains. Assume 40% and equal chances. Just chances by number of sites found and number of paths searched would be great. Seeing the hard numbers would help me think about it, at least.
I'd be very impressed if you could come up with a
nice table with all the probabilities. Way to many variables to format nicely.